EXERCISES. 1 2 y5 2 3 (2y 2 ) 4 2y (3x 5 ) 3 (2x 7 ) 2 108x (210n) 2 (24n 3 ) 3

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1 PRATIE and APPl Assignment Guide Answers for all eercises available online asic: Da : Es., 2, 5 odd, 9 9 odd, 0 2, Average: Da : Es., 2, 8 even, 29 9, 5 58 Advanced: Da : Es., 2, 8 8 even, 8, 0 5*, 5 59* lock: Es., 2, 8 even, 29 9, 5 58 (with net lesson) Differentiated Instruction See Differentiated Instruction Resources for suggestions on addressing the needs of a diverse classroom. Homework heck For a quick check of student understanding of ke concepts, go over the following eercises: asic: 7,, 5, 27, 52 Average: 8, 2, 6,, 5 Advanced: 0,, 8, 6, 5 Etra Practice Student Edition hapter Resource ook: Practice levels A,, Practice Worksheet An easil-readable reduced practice page can be found at the beginning of this chapter. 7. EXAMPLES,2,, and for Es. EXERISES SKILL PRATIE A HOMEWORK KEY. VOAULARY op and complete: The? of the quantit 9,5,00 people is the power of 0 nearest the quantit, or 0 8 people. order of magnitude 2. WRITING Eplain when and how to use the product of powers propert. When powers have the same base, their product is the base raised to the sum of the eponents. SIMPLIFYING EXPRESSIONS Simplif the epression. Write our answer using eponents.. 2 p p p 6. 9 p (2) 7. (27) (27) 5 (27) 9 8. (26) 6 (26) (26) p 2 9 p (2) 2 (2) (2). ( 5 ) (7 ) 7 2. [(25) ] (25) 2. [(28) 9 ] 2 (28) 8 5. (5 p 29) 5 p (7 p 6) 7 p 6 7. (2 p 9) p ((2) p 22) 5 (2) 5 p 22 5 SIMPLIFYING EXPRESSIONS Simplif the epression. 9. p p 0 2. z 2 p z p z z a p a p a 0 a 7 2. ( 5 ) ( ) [(b 2 2) 2 ] 6 (b 2 2) [(d 9) 7 ] (d 9) (25) (5) (7) (5pq) 25p q. (20 6 ) 2 p (28m ) 2 p m 6m. 6d 2 p (2d 5 ) 96d 22. (220 ) 2 (2 7 ) (2p ) (2.5p 7 ) (2 2 ) ( 5 ) (2 7 ) (20n) 2 (2n ) 2p n 9. ERROR ANALYSIS Describe and correct the error in simplifing c p c p c 5. Sample answer: The eponents should be added, not multiplied; c p c p c 5 5 c 5 5 c MULTIPLE HOIE Which epression is equivalent to (29) 6? A (29) 2 (29) (29)(29) 5 [(29) ] 2 D [(29) ]. MULTIPLE HOIE Which epression is equivalent to 6 2? A (6 ) 2 p p ( ) D (6 5 ) 2 p 2 SIMPLIFYING EXPRESSIONS Find the missing eponent. 2. p? 5 5. ( 8 )? (2z? ) 5 8z (a )? p 2a 5 8a POPULATION The population of New York it in 2000 was 8,008,278. What was the order of magnitude of the population of New York it? 0 7 people SIMPLIFYING EXPRESSIONS Simplif the epression. 5 See WORKED-OUT SOLUTIONS Es. and 55 5 STANDARDIZED TEST PRATIE Es. 2, 0,, 50, and 58 5 MULTIPLE REPRESENTATIONS E. 55 c p c p c 5 5 c p c p c 5 5 c p p 5 5 c (2 2 ) ( 5 ) (2 2 z ) 5 ( z) 2 9. (22s)(25r st) (22r st 7 ) z 7 000r 7 s 6 t 7 8 hapter 7 Eponents and Eponential Functions D 8

2 Roalt-Free/Gett Images EXAMPLE 5 A for Es OPEN ENDED Write three epressions involving products of powers, powers of powers, or powers of products that are equivalent to 2 8. Sample answer: 2 p 6, 2( ) 2, (2 ) 2 5. HALLENGE Show that when a and b are real numbers and n is a positive integer, (ab) n 5 a n b n. See margin. PROLEM SOLVING 52. IE REAM OMPOSITION There are about 95,90 air bubbles in cubic centimeter of ice cream. There are about 96 cubic centimeters in quart. Use order of magnitude to find the approimate number of air bubbles in quart of ice cream. 0 9 air bubbles 5. ASTRONOMY The order of magnitude of the radius of our solar sstem is 0 meters. The order of magnitude of the radius of the visible universe is 0 times as great. Find the approimate radius of the visible universe m 5. OASTAL LANDSLIDE There are about billion grains of sand in cubic foot of sand. In 995 a stretch of beach at Sleeping ear Dunes National Lakeshore in Michigan slid into Lake Michigan. Scientists believe that around 5 million cubic feet of sand fell into the lake. Use order of magnitude to find about how man grains of sand slid into the lake. 0 6 grains of sand 55. MULTIPLE REPRESENTATIONS There are about 0 2 atoms of gold in ounce of gold. a. Making a Table op and complete the table b finding the number of atoms of gold for the given amounts of gold (in ounces). Gold (ounces) ,000 00,000 Number of atoms????? b. Writing an Epression A particular mine in alifornia etracted about 96,000 ounces of gold in ear. Use order of magnitude to write an epression ou can use to find the approimate number of atoms of gold etracted in the mine that ear. Simplif the epression. Verif our answer using the table. 0 5 p 0 2 ; 0 28 atoms 56. MULTI-STEP PROLEM A microscope has two lenses, the objective lens and the eepiece, that work together to magnif an object. The total magnification of the microscope is the product of the magnification of the objective lens and the magnification of the eepiece. a. Your microscope s objective lens magnifies an object Eepiece Objective lens 0 2 times, and the eepiece magnifies an object 0 times. What is the total magnification of our microscope? 0 times b. You magnif an object that is 0 2 nanometers long. How long is the magnified image? 0 5 nanometers 7. Appl Eponent Properties Involving Products 9 Vocabular Eercise 2 Encourage students to write out eplanations and give specific eamples for all three properties covered in this lesson. Avoiding ommon Errors Eercises 8 Watch for students who fail to account for numerical or variable bases that have an eponent of. Remind these students that a base without an eponent is raised to the power of and that the need to add or multipl b when simplifing epressions. Also, some students ma overlook the numerical factor when simplifing powers with numerical and variable bases. Remind these students to evaluate the numerical power first. Stud Strateg Eercise 5 You ma want to suggest that students write the standard form of billion and 5 million before the determine the order of magnitude. Students ma want to review order of magnitude and estimation before the begin this eercise. 5. Sample answer: (ab) n 5 (ab) p (ab) p p (ab) so that there are n total factors (ab). the commutative propert, the n a s can be grouped as a repeated multiplication equal to a n and the n b s can be grouped as a repeated multiplication equal to b n. (ab) n is equal to the product of these two groups, or a n p b n. 9

3 5 ASSESS and REtEAch Dail homework Quiz Also available online Simplif the epression. Write our answer using eponents.. 5 p [(28) ] (28) 2 Simplif the epression.. [(m 2 ) 6 ] (m 2 ) 2. 2(2s) 28s 5. A website had about 02 hits after a week. After a ear, it had about 0 times the number of hits of the first week. About how man hits did it have at the end of the ear? about 0,000 hits Online Quiz Available at m.hrw.com Diagnosis/Remediation Practice A,, in hapter Resource ook Stud Guide in hapter Resource ook Practice challenge Additional challenge is available in the hapter Resource ook. 58c. Multiplies the volume b a factor of 0 2. Sample answer: Since the radius is squared in the formula for volume, multipling the radius b 0 would multipl the volume b a factor of 0 p 0, or VOLUME OF THE SUN The radius of the sun is about 695,000,000 meters. The formula for the volume of a sphere, such as the sun, is V 5 πr. ecause the order of magnitude of π is, it does not contribute to the formula in a significant wa. So, ou can find the order of magnitude of the volume of the sun b cubing its radius. Find the order of magnitude of the volume of the sun EXTENDED RESPONSE Rock salt can be mined from large deposits of salt called salt domes. A particular salt dome is roughl clindrical in shape. The order of magnitude of the radius of the salt dome is 0 feet. The order of magnitude of the height of the salt dome is about 0 times Salt that of its radius. The formula for the volume of a clinder is V 5 πr 2 h. a. alculate What is the order of magnitude of the height of the salt dome? 0 b. alculate What is the order of magnitude of the volume of the salt dome? 0 0 c. Eplain The order of magnitude of the radius of a salt dome can be 0 times the radius of the salt dome described in this eercise. What effect does multipling the order of magnitude of the radius of the salt dome b 0 have on the volume of the salt dome? Eplain. 59. HALLENGE Your school is conducting a poll that has two parts, one part that has questions and a second part that has 0 questions. Students can answer the questions in either part with agree or disagree. What power of 2 represents the number of was there are to answer the questions in the first part of the poll? What power of 2 represents the number of was there are to answer the questions in the second part of the poll? What power of 2 represents the number of was there are to answer all of the questions on the poll? 2 was; 2 0 was; 2 2 was 0 See EXTRA PRATIE in Student Resources ONLINE QUIZ at m.hrw.com 0

4 E XAMPLE 5 Solve a real-world problem Etra Eample 5 The order of magnitude of the luminosit of the Milk Wa gala is 0 6 watts. The order of magnitude of the luminosit of a gamma ra burster is 0 5 watts. How man times as luminous is a gamma ra burster as the Milk Wa gala? about 0 9 times as luminous Ke Question Ke Question to Ask for Eample 5Eample 5 How do ou know that ou need to divide to find the solution to this problem? The problem asks for a ratio and ou divide to find ratios. losing the Lesson Have students summarize the major points of the lesson and answer the Essential Question: How do ou use properties of eponents involving quotients? Subtract eponents to divide powers. To find the power of a quotient, find the powers of the numerator and the powers of denominator before dividing. To simplif an epression involving quotients, subtract the eponent of the denominator from the eponent of the numerator. To raise a quotient to a power, find the power of the numerator and the power of the denominator and divide. 7.2 EXAMPLES and 2 for Es. 220 ASTRONOMY The luminosit (in watts) of a star is the total amount of energ emitted from the star per unit of time. The order of magnitude of the luminosit of the sun is 0 26 watts. The star anopus is one of the brightest stars in the sk. The order of magnitude of the luminosit of anopus is 0 0 watts. How man times more luminous is anopus than the sun? Solution Luminosit of anopus (watts) Luminosit of the sun (watts) c anopus is about 0 times as luminous as the sun. GUIDED PRATIE for Eample 5 0. WHAT IF? Sirius is considered the brightest star in the sk. Sirius is less luminous than anopus, but Sirius appears to be brighter because it is much closer to Earth. The order of magnitude of the luminosit of Sirius is 0 28 watts. How man times more luminous is anopus than Sirius? 0 2 EXERISES SKILL PRATIE A. VOAULARY op and complete: In the power, is the? and is the?. base, eponent 2. WRITING Eplain when and how to use the quotient of powers propert. When powers have the same base, their quotient is the base raised to the difference of the eponents. SIMPLIFYING EXPRESSIONS Simplif the epression. Write our answer using eponents (26)8 5 (26) (26) 5 7. (2)7 (22) (2) 9 8. (2) (22) p (22) p HOMEWORK KEY anopus 5 See WORKED-OUT SOLUTIONS Es. and 5 5 STANDARDIZED TEST PRATIE Es. 2, 9, 7, 6, and 5 5 MULTIPLE REPRESENTATIONS E p p p p hapter 7 Eponents and Eponential Functions Differentiated Instruction Advanced In Eample 5, some students ma see that if anopus is 0,000 times as bright as the sun, then the sun is as bright as anopus. hallenge students to use this 0,000 observation to write a ratio of the luminosit of the sun to the luminosit of anopus using eponents. Ask them to eplain their reasoning b describing the relationship between the two ratios. This prepares students for the definition of negative eponents in net lesson. See also the Differentiated Instruction Resources for more strategies. 2 5 ourtes of NASA

5 EXAMPLES, 2, and for Es , 5 2. Sample answer: Using the quotient of a power propert, write two equations for and : 2 5 9, and Solve the equations. 9. MULTIPLE HOIE Which epression is equivalent to 6 6? A ERROR ANALYSIS Describe and correct the error in simplifing 95 p 9. 9 See margin. 2 2 D p SIMPLIFYING EXPRESSIONS Simplif the epression. 2. p z 8 p 2. a 9 7 a z z j k 2 j k 25. p q a b 2 2 q a b 29. c d 2 0. a7 5 6c a 2 2b d 6 2b p p m p m n p m n MULTIPLE HOIE Which epression is equivalent to ? A SIMPLIFYING EXPRESSIONS Find the missing eponent. 8. p D (28) 7 5 (28)? (28) 7 9.? p p p 5 p? 5 p 9. 2c 2? 5 6c2 d 2 d 8 SIMPLIFYING EXPRESSIONS Simplif the epression. 2. 2f 2 g 2s fg 2. t (st) p st 2. s 2 t 2m5 n 2 2 p mn m 2 5n p 2 2 6f g 8 5s t m 8 n OPEN ENDED Write three epressions involving quotients that are equivalent to 7. Sample answer: 8, 0, 7 7. REASONING Name the definition or propert that justifies each step to show that am a n 5 n 2 m for m < n. a Let m < n. a m a n 5 a m a n a m 2 a m? Given 5? a n a m 5 a n 2 m? Identit propert of multiplication Multipl fractions. Quotient of powers propert 8. HALLENGE Find the values of and if ou know that b b 5 b9 and b p b 2 5 b. Eplain how ou found our answer. b 20. Sample answer: When using the quotient of powers propert, the base is raised to the difference of the eponents, not the sum; (8 2 ) Appl Eponent Properties Involving Quotients 5 D PRATIE and APPl Assignment Guide Answers for all eercises available online asic: Da : Es. 28 Da 2: Es. 29 9, 9 52 Average: Da : Es., 2, 7 28, 8 0 Da 2: Es. 7, 6, 9 5 Advanced: Da : Es., 2, 9 9, 2 28, 8 0, 7, 8* Da 2: Es. 2 7, 6, 9 5* lock: Es., 2, 7 28, 8 0 (with previous lesson) Es. 7, 6, 9 5 (with net lesson) Differentiated Instruction See Differentiated Instruction Resources for suggestions on addressing the needs of a diverse classroom. Homework heck For a quick check of student understanding of ke concepts, go over the following eercises: asic: 6, 2, 0, 9, 50 Average: 2, 2, 2, 9, 5 Advanced: 6, 27,, 50, 5 Etra Practice Student Edition hapter Resource ook: Practice levels A,, Practice Worksheet An easil-readable reduced practice page can be found at the beginning of this chapter. 5

6 PROLEM SOLVING Avoiding ommon Errors Eercises 8, 2 6 Watch for students who add eponents when finding a quotient. Remind these students that ou subtract eponents when dividing and add eponents when multipling. EXAMPLES A and 5 for Es MULTIPLE REPRESENTATIONS Draw a square with side lengths that are unit long. Divide it into four new squares with side lengths that are one half the side length of the original square, as shown in Step. Keep dividing the squares into new squares, as shown in Steps 2 and. Stud Strateg Eercises 9, 7 Suggest that students look for was to eliminate answers. In Eercise 9, point out that the can eliminate two choices quickl b subtracting eponents. In Eercise 7, suggest that students evaluate the numerical bases to eliminate two choices. Step 0 Step Step 2 Step a. Making a Table Make a table showing the number of new squares and the side length of a new square at each step for Steps. Write the number of new squares as a power of. Write the side length of a new square as a power of 2. See margin. b. Writing an Epression Write and simplif an epression to find b how man times the number of new squares increased from Step 2 to Step. ; 6 times 2 Mathematical Reasoning Eercises 8 0 For students who have difficult solving these eercises, suggest that the epand numbers and variables into their basic factors and then work backward from what the know. For eample, in Eercise 8, tell them that the know there are 7 factors of (28) in the numerator. The also know that the number of factors in the numerator and denominator cancel so that factors of (28) remain. So the question the need to ask is how man factors of (28) are in the denominator so that onl factors of (28) remain in the numerator after canceling. Internet Reference Eercise 5 More information about earthquakes can be found at pubs.usgs.gov/gip/earthq 50. GROSS DOMESTI PRODUT In 200 the gross domestic product (GDP) for the United States was about trillion dollars, and the order of magnitude of the population of the U.S. was 0 8. Use order of magnitude to find the approimate per capita (per person) GDP. about 0 5 dollars 5. SPAE TRAVEL Alpha entauri is the closest star sstem to Earth. Alpha entauri is about 0 kilometers awa from Earth. A spacecraft leaves Earth and travels at an average speed of 0 meters per second. About how man ears would it take the spacecraft to reach Alpha entauri? about,70 r 52. ASTRONOMY The brightness of one star relative to another star can be measured b comparing the magnitudes of the stars. For ever increase in magnitude of, the relative brightness is diminished b a factor of For instance, a star of magnitude 8 is 2.52 times less bright than a star of magnitude 7. The constellation Ursa Minor (the Little Dipper) is shown. How man times less bright is Eta Ursae Minoris than Polaris? 2.52 times Ursa Minor Eta Ursae Minoris (magnitude 5) 5. EARTHQUAKES The energ released b one earthquake relative to another earthquake can be measured b comparing the magnitudes (as determined b the Richter scale) of the earthquakes. For ever increase of in magnitude, the energ released is multiplied b a factor of about. How man times greater is the energ released b an earthquake of magnitude 7 than the energ released b an earthquake of magnitude? times greater Polaris (magnitude 2) 6 5 See WORKED-OUT SOLUTIONS in Student Resources 5 STANDARDIZED TEST PRATIE 5 MULTIPLE REPRESENTATIONS Akira Fujii/ESA 6 9a. Step Number of new squares Side length of new square

7 QUIZ 5. EXTENDED RESPONSE A bte is a unit used to measure computer memor. Other units are based on the number of btes the represent. The table shows the number of btes in certain units. For eample, from the table ou can calculate that terabte is equivalent to 2 0 gigabtes. a. alculate How man kilobtes are there in terabte? 2 0 kilobtes Unit Number of btes b. alculate How man megabtes are there in Kilobte 2 0 petabte? 2 0 megabtes Megabte 2 20 c. HALLENGE Another unit used to measure computer memor is a bit. There are 8 bits Gigabte 2 0 in a bte. Eplain how ou can convert the Terabte 2 0 number of btes per unit given in the table to the number of bits per unit. Petabte 2 50 Multipl the number of btes in each unit b 8, or 2. Simplif the epression. Write our answer using eponents.. 2 p (5 ) 5 2. (2 p ) p p 7 6 p (2)(2) 9 (2) (29) 9 (29) 2 8. (29) 7 Simplif the epression. 7 p p 5 7. ( ) (7) (6 5 ) p. (2 5 ) (7 7 ) p w v 2 6 w v AGRIULTURE In 200 the order of magnitude of the number of pounds of oranges produced in the United States was 0 0. The order of magnitude of the number of acres used for growing oranges was 0 6. About how man pounds of oranges per acre were produced in the United States in 200? about 0 pounds 5 ASSESS and REtEAch Dail homework Quiz Also available online. Simplif 6 p Simplif 0 7 p Simplif s 8 r 2 s 2 27r. The order of magnitude of the power output of a nuclearpowered aircraft carrier is about 0 6 watts. The order of magnitude of peak power at Hoover Dam is about 0 9 watts. How man times as great is the power output of Hoover Dam as the power output of a nuclearpowered aircraft carrier? 0 Online Quiz Available at m.hrw.com Diagnosis/Remediation Practice A,, in hapter Resource ook Stud Guide in hapter Resource ook Practice challenge Additional challenge is available in the hapter Resource ook. Quiz An easil-readable reduced cop of the quiz from the Assessment ook can be found at the beginning of this chapter. See EXTRA PRATIE in Student Resources ONLINE QUIZ at m.hrw.com 7 7

8 PRATIE and APPl Assignment Guide Answers for all eercises available online asic: Da : Es., 2, 5 odd, Average: Da : Es., 2, 9, 2 27, 28 even, 5, 5 57 Advanced: Da : Es., 2,, 22 26, 29 odd, 9*, 52 58* lock: Es., 2, 9, 2 27, 28 even, 5, 5 57 (with previous lesson) Differentiated Instruction See Differentiated Instruction Resources for suggestions on addressing the needs of a diverse classroom. Homework heck For a quick check of student understanding of ke concepts, go over the following eercises: asic: 5, 9, 25, 29, 5 Average: 0, 22, 26,, 52 Advanced: 2, 2,,, 5 Etra Practice Student Edition hapter Resource ook: Practice levels A,, Practice Worksheet An easil-readable reduced practice page can be found at the beginning of this chapter. 7. EXAMPLE for Es. EXAMPLE 2 for Es EXAMPLE for Es. 28 EXERISES SKILL PRATIE A. VOAULARY Which definitions or properties would ou use to simplif the epression 5 p 25? Eplain. Product of powers propert and definition of zero eponent; the epression simplifies using the product of powers propert to 0, which b definition equals. 2. WRITING Eplain wh the epression 0 2 is undefined. Sample answer: The definition of negative eponents is defined onl for nonzero bases. EVALUATING EXPRESSIONS Evaluate the epression (2) (22) (2) undefined undefined p p 7 7. (2 2 ) 5 8. ( 22 ) p p ERROR ANALYSIS Describe and correct the error in evaluating the epression 26 p 0. 0 is not equivalent to 0, but to ; 26 p p SIMPLIFYING EXPRESSIONS Simplif the epression. Write our answer using onl positive eponents (g) 2. (2h) g. 5m 2 n 2 5. (6 22 ) 2 6 2h 2 5. (25fg 2 ) 0 m n 26 9 r s s r z 2. (22z) 22 () d (d) 2. MULTIPLE HOIE Which epression simplifies to 2? A (2) D MULTIPLE HOIE Which epression is equivalent to (2 p 2 0 p ) 22? D A 22 2 HOMEWORK KEY 26 p p See WORKED-OUT SOLUTIONS Es. and 5 5 STANDARDIZED TEST PRATIE Es. 2,, 5, 5, and 57 5 MULTIPLE REPRESENTATIONS E D D hapter 7 Eponents and Eponential Functions 52

9 center left arln Iverson/Photo Researchers, Inc.; center right mediacolor s/alam 6. Not true. Sample answer: 2 2 EXAMPLE A for Es HALLENGE In Eercises 628, tell whether the statement is true for all nonzero values of a and b. If it is not true, give a countereample a 6. a 5 a 7. 2 a b true 8. a 2 b 2 5 b 2 a 8. Not true. 9. HALLENGE ompare the values of a n and a 2n when n < 0, when n 5 0, Sample answer: and when n > 0 for (a) a > and (b) 0 < a <. Eplain our reasoning See margin. PROLEM SOLVING 50. MASS The mass of a grain of salt is about 0 2 gram. About how man grains of salt are in a bo containing 00 grams of salt? about 0 6 grains of salt 5. MASS The mass of a grain of a certain tpe of rice is about 0 22 gram. About how man grains of rice are in a bo containing 0 grams of rice? about 0 5 grains of rice a b 52. OTANY The average mass of the fruit of the wolffia angusta plant is about 0 2 gram. The largest pumpkin ever recorded had a mass of about 0 kilograms. About how man times greater is the mass of the largest pumpkin than the mass of the fruit of the wolffia angusta plant? about 0 times greater 5. MEDIINE A doctor collected about 0 22 liter of blood from a patient to run some tests. The doctor determined that a drop of the patient s blood, or about 0 26 liter, contained about 0 7 red blood cells. How man red blood cells did the entire sample contain? about 0 red blood cells 5. SHORT RESPONSE One of the smallest plant seeds comes from an orchid, and one of the largest plant seeds comes from a giant fan palm. A seed from an orchid has a mass of 0 29 gram and is 0 times less massive than a seed from a giant fan palm. A student sas that the seed from the giant fan palm has a mass of about kilogram. Is the student correct? Eplain. No. Sample answer: The giant fan palm has a mass of about 0 grams or 0,000 grams, which Orchid Giant fan palm equals 0 kilograms. 55. MULTIPLE REPRESENTATIONS onsider folding a piece of paper in half a number of times. a. Making a Table Each time the paper is folded, record the number of folds and the fraction of the original area in a table like the one shown. Number of folds 0 2 Fraction of original area???? 2 8 b. Writing an Epression Write an eponential epression for the fraction of the original area of the paper using a base of where is the number of folds 7. Define and Use Zero and Negative Eponents 5 Avoiding ommon Errors Eercises 26, 28 Students often evaluate an epression with an eponent of zero as equal to 0. Remind these students that an nonzero epression with an eponent of 0 is equal to. Eercises 28 aution students to distinguish between a negative number or variable in the base of an epression and a negative eponent. Remind them that the take the reciprocal when the eponent in a power is negative, not when the base is negative. Stud Strateg Eercises 28 Tell students that a variet of strategies and steps can be used to solve these problems and that the best strateg overall is to take their time in simplifing the epressions. Urge them to pa attention to the sign of the eponent, to epressions in parentheses, and to whether an eponent applies to a number or variable. Remind them that the can alwas epand factors if necessar. Mathematical Reasoning Eercises 50, 5 You ma want to point out to students that the can determine a reasonable answer to these eercises b asking how man grains of salt are in gram of salt and how man grains of rice are in gram of rice. Suggest that the first write the mass of the grains of salt and rice using positive eponents, then determine how man grains are in a gram, and finall multipl b the number of respective grams in the boes of salt and rice. 9a. For a >, when n < 0, 2n > 0, so a n is between 0 and, a 2n is greater than, and a n < a 2n. When n 5 0, a n 5 a 0 5 and a 2n 5 a 0 5, so a n 5 a 2n. When n > 0, 2n < 0, so a n is greater than, a 2n is between 0 and, and a n > a 2n. b. For 0 < a <, when n < 0, 2n > 0, so a n is a whole number, a 2n is a fraction, and a n > a 2n. When n 5 0, a n 5 a 0 5 and a 2n 5 a 0 5, so a n 5 a 2n. When n > 0, n < 0, so a n is a fraction, a 2n is a whole number, and a n < a 2n. 5

10 5 ASSESS and REtEAch Dail homework Quiz Also available online. Evaluate Evaluate 27 p Simplif 6a 2 b 0 6. a. Simplif A human cell uses on average about 0 22 watt of power. The laser in a D-R drive uses about 0 9 times as man watts. About how man watts of power does the laser in a D-R drive use? about 0 2 Online Quiz Available at m.hrw.com Diagnosis/Remediation Practice A,, in hapter Resource ook Stud Guide in hapter Resource ook Practice challenge Additional challenge is available in the hapter Resource ook. 56. SIENE Diffusion is the movement of molecules from one location to another. The time t (in seconds) it takes molecules to diffuse a distance of centimeters is given b t 5 2 where D is the diffusion coefficient. 2D a. You can eamine a cross section of a drop of ink in water to see how the ink diffuses. The diffusion coefficient for the molecules in the drop of ink is about 0 25 square centimeter per second. How long will it take the ink to diffuse micrometer (0 2 centimeter)? sec (cm) 2 b. heck our answer to part (a) using unit analsis. 5 cm 2 sec p 5 sec cm 2 cm 2 sec 57. EXTENDED RESPONSE The intensit of sound I (in watts per square meter) can be modeled b I Pd 22 where P is the power (in watts) of the sound s source and d is the distance (in meters) that ou are from the source of the sound. I = 0 2 watts per square meter (at hearer s ear) d = 0 meters Not to scale a. What is the power (in watts) of the siren of the firetruck shown in the diagram? 2.5 watts b. Using the power of the siren ou found in part (a), simplif the formula for the intensit of sound from the siren. I 5 9d 22 c. Eplain what happens to the intensit of the siren when ou double our distance from it. The intensit is divided b. 58. HALLENGE oal can be burned to generate energ. The heat energ in pound of coal is about 0 TU (ritish Thermal Units). Suppose ou have a stereo. It takes about 0 pounds of coal to create the energ needed to power the stereo for ear. a. About how man TUs does our stereo use in ear? 0 5 TUs b. Suppose the power plant that delivers energ to our home produces 0 2 pound of sulfur dioide for each 0 6 TU of energ that it creates. How much sulfur dioide is added to the air b generating the energ needed to power our stereo for ear? 0.0 lb 5 See EXTRA PRATIE in Student Resources ONLINE QUIZ at m.hrw.com 5

11 ESTIMATE You can use the simple interest formula, I 5 prt, to estimate the amount of interest earned: (250)(0.0)(5) ompounding interest will result in slightl more than $ OMPOUND INTEREST ompound interest is interest earned on both an initial investment and on previousl earned interest. ompounding of interest can be modeled b eponential growth where a is the initial investment, r is the annual interest rate, and t is the number of ears the mone is invested. E XAMPLE 5 Standardized Test Practice You put $250 in a savings account that earns % annual interest compounded earl. You do not make an deposits or withdrawals. How much will our investment be worth in 5 ears? A $00 $0.6 $.56 D $78,250 Solution 5 a( r) t Write eponential growth model ( 0.0) 5 Substitute 250 for a, 0.0 for r, and 5 for t (.0) 5 Simplif. ø 0.6 Use a calculator. You will have $0.6 in 5 ears. c The correct answer is. A D GUIDED PRATIE for Eamples and 5 5. WHAT IF? In Eample, suppose the owner of the car sold it in 99. Find the value of the car to the nearest dollar. $2,7 6. WHAT IF? In Eample 5, suppose the annual interest rate is.5%. How much will our investment be worth in 5 ears? $ EXERISES SKILL PRATIE A HOMEWORK KEY 5 See WORKED-OUT SOLUTIONS Es. and 5 STANDARDIZED TEST PRATIE Es., 8, 5, 2,, 6, and 50 5 MULTIPLE REPRESENTATIONS Es.,. VOAULARY In the eponential growth model 5 a( r) t, the quantit r is called the?. growth factor 2. VOAULARY For what values of b does the eponential function 5 ab (where a > 0) represent eponential growth? b >. WRITING How does the graph of 5 2 p 5 compare with the graph of 5 5? Eplain. The graph would be a vertical stretch. Sample answer: Since the -values of 5 2 p 5 are double those of 5 5. Etra Eample 5 You put $25 in a savings account that earns 2% interest compounded earl. You do not make an deposits or withdrawals. How much will our investment be worth in 5 ears? A $0 $8.0 $.0 D $000 Ke Question Ke Question to Ask for Eample 5Eample 5 Wh is an estimate using the simple interest formula useful? Since it shows that simple interest is $50 and compound interest would be slightl more than $50, ou can eliminate all answer choices ecept. losing the Lesson Have students summarize the major points of the lesson and answer the Essential Question: How do ou write and graph equations for eponential growth functions? An eponential function has the form 5 ab, where a? 0, b > 0, and b?. The eponential growth model is 5 a ( r) t, where a is the initial amount, r is the growth rate, and t is the time period. Use the eponential growth model to write an equation. Substitute the initial amount for a, the rate for r, written as a decimal, and the time period for t. When graphing an eponential function, make a table of negative and positive values, determine the -intercept, plot the points on a coordinate plane, and connect them with a smooth curve. Differentiated Instruction 7. Write and Graph Eponential Growth Functions 6 :2:58 PM Advanced Suggest that students research several banks, either locall or online, for interest rates on savings accounts, mone market accounts, and Ds. Have them develop eponential growth models for each tpe of account at each bank on an initial deposit of $500 after 2 ears. Ask students to make a chart comparing the rates and potential earnings for the different tpes of accounts and the different banks. See also the Differentiated Instruction Resources for more strategies. 6

12 PRATIE and APPl Assignment Guide Answers for all eercises available online asic: Da : SRH p. SR5, Es. 9 Es. 2 Da 2: Es , 8 Average: Da : Es. 8, 2, 5 Da 2: Es. 22, 8 6 Advanced: Da : Es., 2, 8, 2, 5 7* Da 2: Es. 26, 9 5* lock: Es. 8, 5, 8 6 Differentiated Instruction See Differentiated Instruction Resources for suggestions on addressing the needs of a diverse classroom. Homework heck For a quick check of student understanding of ke concepts, go over the following eercises: asic:, 2, 2, 8, 9 Average: 5, 6, 28, 8, 0 Advanced: 6, 20, 2, 9, Etra Practice Student Edition hapter Resource ook: Practice levels A,, Practice Worksheet An easil-readable reduced practice page can be found at the beginning of this chapter. EXAMPLE for Es p p p p EXAMPLE 2 for Es The percent increase was not written as a decimal; 0.27( 0.02) (.02) ø $.29. EXAMPLE for Es %. Sample answer: A growth rate of 200% would create a growth factor of 2 5, which would represent the tripling of the population ever ear. 7. Sample answer: The graphs are the same. Since b the product of a power propert p 2 2, and 2 p 2 2 simplifies to p 2, p WRITING FUNTIONS Write a rule for the function WRITING Given a table of values, describe how can ou tell if the table represents a linear function or an eponential function. See margin. GRAPHING FUNTIONS Graph the function and identif its domain and range See margin (.5). 5 (2.5) 5. 5 (.2) 6. 5 (.) ERROR ANALYSIS The price P (in dollars) of a pound of flour was $.27 in 999. The price has increased b about 2% each ear. Let t be the number of ears since 999. Describe and correct the error in finding the price of a pound of flour in OMPARING GRAPHS OF FUNTIONS Graph the function. ompare the graph with the graph of See margin p 2. 5 p 2. 5 p p p p p p p p p p. MULTIPLE REPRESENTATIONS Given the function 5 a, ou can find when 5 k b solving the eponential equation k 5 a. Use the following methods to solve a, b. See margin. a. Making a Table Make a table for the function using 5 0,, 2,..., 6. b. Graphing Functions Graph the functions 5 2 and 5 2 on the same coordinate plane. Identif the -coordinate of the intersection point. c. Using Powers Write 2 as a power of 2. Then use the fact that powers with the same base are equal provided that their eponents are equal p 2 p 2 p 2 p ; because , must equal WRITING If a population triples each ear, what is the population s growth rate (as a percent)? Eplain. 6. HALLENGE Write a linear function and an eponential function whose graphs pass through the points (0, 2) and (, 6). Sample answer: f() 5 2, f() 5 2 p 7. HALLENGE ompare the graphs of the functions f() and g() 5 p 2. Use properties of eponents to eplain our observations. 5 See WORKED-OUT SOLUTIONS in Student Resources 27 9 P 5 a( r) t ( 2) () In 2002 the price of a pound of flour was $ STANDARDIZED TEST PRATIE 5 MULTIPLE REPRESENTATIONS 8. Sample answer: If the difference between successive terms is constant, the function is linear and if the ratio of successive terms is constant, the function is eponential. 9 20, 22. See Additional Answers. 62

13 PROLEM SOLVING EXAMPLES A and 5 for Es. 8 9a. Let represent the number of ears since 200 and f() represent the number of computers (in hundreds of millions); f() 5 6 p (.). 0a. Let represent the number of ears since 985 and f() represent the number of grills shipped; f() 5,7,000 p (.07). GRAPHING ALULATOR You ma wish to use a graphing calculator to complete the following Problem Solving eercises. 8. INVESTMENTS You deposit $25 in a savings account that earns 5% annual interest compounded earl. Find the balance in the account after the given amounts of time. a. ear $.25 b. 2 ears $7.8 c. 5 ears $59.5 d. 20 ears $ MULTI-STEP PROLEM One computer industr epert reported that there were about 600 million computers in use worldwide in 200 and that the number was increasing at an annual rate of about 0%. a. Write a function that models the number of computers in use over time. b. Use the function to predict the number of computers that will be in use worldwide in about,286,5,286 computers 0. MULTI-STEP PROLEM A research association reported that,7,000 gas grills were shipped b various manufacturers in the U.S. in 985. Shipments increased b about 7% per ear from 985 to a. Write a function that models the number of gas grills shipped over time. b. About how man gas grills were shipped in 2002? about 0,022,92 gas grills. MULTIPLE REPRESENTATIONS A tree s cross-sectional area taken at a height of.5 feet from the ground is called its basal area and is measured in square inches. Tree growth can be measured b the growth of the tree s basal area. The initial basal area and annual growth rate for two particular trees are shown. Avoiding ommon Errors Eercises 6 Some students ma fail to find the value of a. Remind students that an eponential function is in the form of 5 ab and that the can find the value of a b finding the value of when 5 0. Eercises 8 Watch for students who do not write percents as decimals before appling the eponential growth model. Graphing alculator Eercises 9 20, 22 Students ma want to check their graphs on a graphing calculator. The can enter the function in the Y 5 menu and then press Graph. The can press Table to check values. The can scroll up or down to see more values. Reading Strateg Eercises 8 Draw students attention to the graphing calculator logo at the top of the page. Point out that the logo appears whenever a graphing calculator is suggested for the eercises. b. A tree tree 2 50 t a. Writing a Model Write a function that models the basal area A of each tree over time. tree : A 5 5 p (.06) t, tree 2: A 5 p (.) t b. Graphing a Function Use a graphing calculator to graph the functions from part (a) in the same coordinate plane. In about how man ears will the trees have the same basal area? See margin for art; about 8. r. 7. Write and Graph Eponential Growth Functions 6 a b. c p 2 p 2 p 2 p ; because , must equal 5. Intersection =5 Y=2 6

14 Avoiding ommon Errors Eercises 2 6 Some students ma forget to add to the rate of growth in the eponential growth model. Remind students that r is the growth factor in the model. Stud Strateg Eercises 7 50 Encourage students to stud the Eample in the net page in detail. You ma wish to present this Eample to students to be certain the understand what each variable in the formula represents. b Yes. Sample answer: The quotient of each pair of adjacent terms is the same, 7. a. initial amount:.67 million, growth factor:.65, growth rate: 0.65 b. See margin for art; domain: 0 0, range:.67 million million (.059) ; about 5 Hz 2. SHORT RESPONSE A compan sells advertising blimps. The table shows the costs of advertising blimps of different lengths. Does the table represent an eponential function? Eplain. Length, l (feet) ost, c (dollars) MULTIPLE HOIE A weblog, or blog, refers to a website that contains a personal journal. According to one analst, over one 8 month period, the number of blogs in eistence doubled about ever 6 months. The analst estimated that there were about 600,000 blogs at the beginning of the period. How man blogs were there at the end of the period? A 660,000,200,000,800,000 D 6,200,000. TELEOMMUNIATIONS For the period , the number (in millions) of Internet users worldwide can be modeled b the function 5.67(.65) where is the number of ears since 99. a. Identif the initial amount, the growth factor, and the growth rate. b. Graph the function. Identif its domain and range. c. Use our graph from part (b) to graph the line 5 2. Estimate the ear in which the number of Internet users worldwide was about 2 million. 5. GRAPHING ALULATOR The frequenc (in hertz) of a note plaed on a piano is a function of the position of the ke that creates the note. The position of some piano kes and the frequencies of the notes created b the kes are shown below. Use the eponential regression feature on a graphing calculator to find an eponential model for the frequenc of piano notes. What is the frequenc of the note created b the 0 th ke? 99 6c. Sample answer: The eponential model is more accurate from The eponential model underestimates the actual totals b less than 2 million in 850 and 870, while the linear model overestimates b more than 5 million in each ear. Ke Frequenc (in hertz) EXTENDED RESPONSE In 80, the population of the United States was 2,866, , the population was 62,97,7. a. Model Assume the population growth from 80 to 890 was linear. Write a linear model for the U.S. population from 80 to 890. about how much did the population grow per ear from 80 to 890? ,866,020; people b. Model Assume the population growth from 80 to 890 was eponential. Write an eponential model for the U.S. population from 80 to 890. approimatel what percent did the population grow per ear from 80 to 890? 5 2,866,020(.0268) ; about 2.68% c. Eplain The U.S. population was 2,9,876 in 850 and 8,558,7 in 870. Which of the models in parts (a) and (b) is a better approimation of actual U.S. population for the time period ? Eplain. See margin STANDARDIZED TEST PRATIE 6

15 50. Dail; in an account compounded dail, each da ou earn interest on both the principal and the interest that was accrued on the previous das. OMPOUND INTEREST In Eercises 7 9, use the eample below to find the balance of the account compounded with the given frequenc. E XAMPLE Use the general compound interest formula FINANE You deposit $000 in an account that pas % annual interest. Find the balance after 8 ears if the interest is compounded monthl. Solution r The general formula for compound interest is A 5 P n 2 nt. In this formula, P is the initial amount, called principal, in an account that pas interest at an annual rate r and that is compounded n times per ear. The amount A (in dollars) is the amount in the account after t ears. Here, the interest is compounded monthl. So, n 5 2. r A 5 P n 2 nt Write compound interest formula (8) Substitute 000 for P, 0.0 for r, 2 for n, and 8 for t (.0025) 96 Simplif. ø Use a calculator. c The account balance after 8 ears will be about $ Yearl $ Quarterl $ Dail (n 5 65) $ WRITING Which compounding frequenc ields the highest balance in the account in the eample above: monthl, earl, quarterl, or dail? Eplain wh this is so. 5. HALLENGE The value (in dollars) of an investment of $000 is given b 5 000(.05) t where t is the time in ears. The doubling time is the value of t for which the amount invested doubles, so that 000(.05) t , or (.05) t 5 2. Graph the functions 5 (.05) t and 5 2 on a graphing calculator. Estimate the doubling time. about ears 5 ASSESS and REtEAch Dail homework Quiz Also available online. Graph Your famil bought a house for $50,000 in The value of the house increases at an annual rate of 8%. What is the value of the house after 5 ears? about $220,99 Online Quiz Available at m.hrw.com Diagnosis/Remediation Practice A,, in hapter Resource ook Stud Guide in hapter Resource ook Practice challenge Additional challenge is available in the hapter Resource ook. See EXTRA PRATIE in Student Resources ONLINE QUIZ at m.hrw.com 65 65

16 7.5 EXAMPLE for Es. 6 EXAMPLE 2 for Es. 7 8 EXAMPLE for Es. 9 EXERISES SKILL PRATIE A 2. Sample answer: If the graph increases from left to right, then it represents growth; if it decreases from left to right, then it represents deca.. VOAULARY What is the deca factor in the eponential deca model 5 a( 2 r) t? r 2. WRITING Eplain how ou can tell if a graph represents eponential growth or eponential deca. See margin. WRITING FUNTIONS Tell whether the table represents an eponential function. If so, write a rule for the function eponential function; 5 8 p eponential function; 5 0(0.2) eponential function; not an eponential function GRAPHING FUNTIONS Graph the function and identif its domain and range See margin (0.). 5 (0.5) 5. 5 (0.) 6. 5 (0.9) 7. 5 (0.7) 8. 5 (0.25) 9. MULTIPLE HOIE The graph of which function is shown? D A 5 (0.25) 5 (0.5) p (0.5) D 5 p (0.5) (0, ) OMPARING FUNTIONS Graph the function. ompare the graph with the graph of See margin p p (, 2) p p p p p p p p HOMEWORK KEY 5 See WORKED-OUT SOLUTIONS Es. 7 and 9 5 STANDARDIZED TEST PRATIE Es. 2, 9, 6, 5, and 9 5 MULTIPLE REPRESENTATIONS E p p Write and Graph Eponential Deca Functions 7 PRATIE and APPl Assignment Guide Answers for all eercises available online asic: Da : Es. 8 Da 2: Es. 9 5 odd, 6 0, 7 50 Average: Da : Es. 6, 0 8, 2 Da 2: Es. 9, 20 0 even, 5, 7 52 Advanced: Da : Es., 6, 2 8, 2 7 Da 2: Es. 9, 2, 8 5* lock: Es. 6, 0 9, 20 0 even, 2, 7 52 Differentiated Instruction See Differentiated Instruction Resources for suggestions on addressing the needs of a diverse classroom. Homework heck For a quick check of student understanding of ke concepts, go over the following eercises: asic:, 8, 2, 8, 7 Average: 5, 2, 2, 9, 8 Advanced: 6, 6, 28, 0, 9 Etra Practice Student Edition hapter Resource ook: Practice levels A,, Practice Worksheet An easil-readable reduced practice page can be found at the beginning of this chapter. :25:2 PM 7 8, 20. See Additional Answers. 7

17 Avoiding ommon Errors Eercises 7 8 Some students graphs ma cross the -ais. Remind these students that graphs of eponential functions get closer and closer to the -ais, but do not cross it. Graphing alculator Eercises 20 Students ma want to use their graphing calculators to compare the graphs. Remind them to use parentheses around the fractions and carets to indicate the eponent. Algebra m.hrw.com An Animated Algebra activit is available online for Eercise 8. This activit is also part of Power Presentations. 5. initial amount: 90,000 people, deca factor: 0.975, deca rate: 2.5%; Let P represent the population and t represent the number of ears. P 5 90,000(0.975) t 5. To find t, divide the number of das, 0, b the half-life, 0. Then A 5 00(0.5) grams. EXAMPLE for Es The deca rate, r, is 0.. So the deca factor ( 2 r) should be 0.86, not 0.; 5 25,000(0.86) t. 8. eponential deca; 5 6 p 0.8 b. The graph is a vertical stretch with a reflection in the -ais. c. The graph is a vertical shift up unit. 6. Sample answer: The graphs are the same. the product of powers propert, p 22, or 6 p. MATHING Match the function with its graph (0.2). 5 5(0.2) A. 5 2 (0.2) A POPULATION A population of 90,000 decreases b 2.5% per ear. Identif the initial amount, the deca factor, and the deca rate. Then write a function that models the population over time. See margin. 6. MULTIPLE HOIE What is the deca rate of the function 5 (0.97) t? A D ERROR ANALYSIS In 200 a person purchased a car for $25,000. The value of the car decreased b % annuall. Describe and correct the error in writing a function that models the value of the car since a( 2 r) t 5 25,000(0.) t REOGNIZING EXPONENTIAL MODELS Tell whether the graph represents eponential growth or eponential deca. Then write a rule for the function (0, 6) (,.8) at m.hrw.com 9. 5 (0, 8) (,.8). REASONING Without graphing, eplain how the graphs of the given functions are related to the graph of f() 5 (0.5). 0. (0, 8) (, 2.8) a. m() 5 p (0.5) b. n() 5 2 p (0.5) c. p() 5 (0.5) The graph is a vertical shrink. HALLENGE Write an eponential function of the form 5 ab whose graph passes through the given points. 2. (0, ), 2, eponential deca; 5 8 p (, 20), (2, )., 5 2 2, 2, p 52 5 p WRITING The half-life of a radioactive substance is the time required for half the substance to deca. The amount A (in grams) of a 00 gram sample of a radioactive substance remaining after t half-lives is given b A 5 00(0.5) t. Suppose the substance has a half-life of 0 das. Eplain how to find the amount left after 0 das. Then find the amount. See margin. 6. HALLENGE ompare the graphs of the functions f() and g() 5 6 p. Use properties of eponents to eplain our observation. 2 D eponential growth; 5 8 p See WORKED-OUT SOLUTIONS in Student Resources 5 STANDARDIZED TEST PRATIE 5 MULTIPLE REPRESENTATIONS 7

18 PROLEM SOLVING EXAMPLE 5 A for Es a. initial amount:,200; deca factor: 0.89; deca rate: % 8b. Let represent the number of bats and t represent the number of ears since 98, 5,200 (0.89) t ;,729 bats. GRAPHING ALULATOR You ma wish to use a graphing calculator to complete the following Problem Solving eercises. 7. ELL PHONES You purchase a cell phone for $25. The value of the cell phone decreases b about 20% annuall. Write a function that models the value of the cell phone over time. Then find the value of the cell phone after ears. Let V represent the value of the cell phone and t represent the number of ears since purchase, V 5 25(0.8) t ; $6. 8. ANIMAL POPULATION Scientists studied the population of a species of bat in some caves in Missouri from 98 to 200. In 98, there were,200 bats living in the caves. That number decreased b about % annuall until 200. a. Identif the initial amount, the deca factor, and the deca rate. b. Write a function that models the number of bats since 98. Then find the number of bats in 200. Stud Strateg Eercise 8 Suggest that students use the eponential deca model given in the lesson to check their solutions to parts (a) and (b). Vocabular Eercise 9 You ma want to ask a student to use a dictionar or thesaurus to define the word depreciate. Have the student look up the word appreciate as an antonm to depreciate. Then ask them to discuss the relationship of these terms to eponential functions. Internet Reference 9. SHORT RESPONSE In 200 a famil bought a boat for $000. The boat depreciates (loses value) at a rate of 7% annuall. In 2006 a person offers to bu the boat for $000. Should the famil sell the boat? Eplain. No. Sample answer: The boat s value is about $ MULTIPLE REPRESENTATIONS There are a total of 28 teams at the start of a citwide -on- basketball tournament. Half of the teams are eliminated after each round. a. Writing a Model Write a function for the number of teams left after rounds. f() 5 28(0.5) b. Making a Table Make a table for the function using 5 0,, 2,..., 7. See margin. c. Drawing a Graph Use the table in part (b) to graph the function. After which round are there teams left in the tournament? See margin for art; round GUITARS The frets on a guitar are the small metal bars that divide the fingerboard. The distance d (in inches) between the nut and the first fret or an two consecutive frets can be modeled b the function d 5.56(0.99) f where f is the number of the fret farthest from the nut. Eercise 5 More information about maimal ogen consumption can be found at org/phscor/ma_o2.html 50b. Rounds completed Teams remaining Fret Nut (tr), Scott Johnson/Indiana DNR/USFWS; (b), Stockbte/Gett Images 5a. deca factor: 0.99, deca rate: 5.6% a. Identif the deca factor and the deca rate for the model. b. What is the distance between the nut and the first fret? about. in. c. The distance between the 2th and th frets is about half the distance between the nut and the first fret. Use this fact to find the distance between the 2th and th frets. Use the model to verif our answer. about 0.76 in. 7.5 Write and Graph Eponential Deca Functions 75 50c. 0 2 nan t 75

19 5 ASSESS and REtEAch Dail homework Quiz Also available online. Graph The population in a town has been declining at a rate of 2% per ear since 200. The population was 8,22 in 200. What was the population in 2006? about 76,0 52. HALLENGE A college student finances a computer that costs $850. The financing plan states that as long as a minimum monthl pament of 2.25% of the remaining balance is made, the student does not have to pa interest for 2 months. The student makes onl the minimum monthl paments until the last pament. What is the amount of the last pament if the student bus the computer without paing interest? Round our answer to the nearest cent. $ MULTI-STEP PROLEM Maimal ogen consumption is the maimum volume of ogen (in liters per minute) that the bod uses during eercise. Maimal ogen consumption varies from person to person and decreases with age b about 0.5% per ear after age 25 for active adults. a. Model A 25-ear-old female athlete has a maimal ogen consumption of liters per minute. Another 25-ear-old female athlete has a maimal ogen consumption of.5 liters per minute. Write a function for each athlete that models the maimal consumption each ear after age (0.995), 5.5(0.995) b. Graph Graph the models in the same coordinate plane. See margin. c. Estimate About how old will the first athlete be when her maimal ogen consumption is equal to what the second athlete s maimal ogen consumption is at age 25? about 52 r Online Quiz Available at m.hrw.com Diagnosis/Remediation Practice A,, in hapter Resource ook Stud Guide in hapter Resource ook Practice challenge Additional challenge is available in the hapter Resource ook. Quiz An easil-readable reduced cop of the quiz from the Assessment ook can be found at the beginning of this chapter.. Let V represent the value of the coin and t represent the number of ears since purchase, V 5 25(.08) t ; about $5.97. QUIZ Simplif the epression. Write our answer using onl positive eponents.. (2) p (2) ( ) 2 6 (6) (5z) z Graph the function See margin p p 8. 5 (0.) p (0.). OINS You purchase a coin from a coin collector for $25. Each ear the value of the coin increases b 8%. Write a function that models the value of the coin over time. Then find the value of the coin after 0 ears. Round to the nearest cent. 5b. 5 (0.995) 5.5(0.995) 76 See EXTRA PRATIE in Student Resources ONLINE QUIZ at m.hrw.com Jon Rile/Gett Images 5 Quiz 5 0. See Additional Answers. 76