Lesson 6.1 Recursive Routines

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1 Lesson 6. Recursive Routines. Give the starting value and constant multiplier for each sequence. Then find the fifth term. a. 4800, 200, 300,... b. 2, 44., 92.6,... c. 00, 90, 8,... d. 00, 0, 02.0,... e.,., 0.4,... f. 3., 0.3, 0.03, Use a recursive routine to find the first five terms of the sequence with the given starting value and constant multiplier. a. Starting value: 2; multiplier:. b. Starting value: 360; multiplier: 0.8 c. Starting value: 4; multiplier: 3 d. Starting value: 9; multiplier: 2.2 e. Starting value:.; multiplier: 2 3. Use a recursive routine to find the first five terms of the sequence with the given starting value and percent increase or decrease. a. Starting value: 6; increases b 0% with each term b. Starting value: 24,000; decreases b 80% with each term c. Starting value: 7; increases b 00% with each term d. Starting value: 40; increases b 20% with each term e. Starting value: 00,000; decreases b 3% with each term 4. Use the distributive propert to rewrite each epression in an equivalent form. For eample, ou can write 00( 0.0) as 00 00(0.0). a (0.8) b. 0 0(0.03) c. W Ws d. 2( 0.04) e. 3 3(0.9) f. 0( 0.2) g. (0.2) h. 0.02( 0.) i. 0,000( 0.0). Burke s Discount Clothing has a Must Go rack. The price of each item on the rack is decreased b 0% each da until the item is sold. On Februar 2, a leather jacket on the rack is priced at $4.00. a. Write a recursive routine to show the price of the jacket on subsequent das. b. What will the jacket cost on Februar 6? c. When will the jacket be priced less than $20.00? 42 Discovering Algebra More Practice Your Skills 2007 Ke Curriculum Press

2 Lesson 6.2 Eponential Equations. Rewrite each epression with eponents. a. (2.)(2.)(2.)(2.)(2.) b. (8)(8)(8)(9)(9)(9)(9)(9)(9) c. ( 0.07)( 0.07)( 0.07) d An investment of $700 increases b 0.3% each month. a. What is the value of the investment after months? b. What is the value after ear? 3. A population of 2,000 increases b.2% each ear. a. What is the population after 4 ears? b. What is the population after 84 months? 4. Match each equation with a table of values. a. 3(0.09) b. 4(.03) c. (0.7) i. ii. iii Match each recursive routine with the equation that gives the same value. a..2 ENTER, Ans 0.7 ENTER i..2(.2) b. 0.7 ENTER, Ans ( 0.2) ENTER ii. 0.7(0.7) c..2 ENTER, Ans Ans 0.2 ENTER iii. 0.7(.2) d. 0.7 ENTER, Ans ( 0.2) ENTER iv..2( 0.2) 6. The equation 2,000( 0.04) models the salar of an emploee who receives an annual raise. Give the meaning of each number and variable in this equation For each table, find the value of the constants a and b such that a b. a. b. c Ke Curriculum Press Discovering Algebra More Practice Your Skills 43

3 Lesson 6.3 Multiplication and Eponents. Use the properties of eponents to rewrite each epression. Use our calculator to check that our epression is equivalent to the original epression. a. (7)(w)(w)(w)(w) b. (3)(a)(a)(a)(b)(b)(b)(b)(b) c. ()(p)(p)(p)(3)(q)(q) d e. (6c)2c 3 3d 2 f. 4m 3 2m m 2 2. Write each epression in epanded form. Then rewrite the product in eponential form. a b. (3) (3) 2 c. (2) 8 (2) 7 d e. 9 4 f. n n 9 3. Rewrite each epression with a single eponent. a. 4 b c. 9 4 d. 3 0 e. 3 7 f g. z 8 2 h i j k. 6 4 l. t Use the properties of eponents to rewrite each epression. a. 4 3 b. (6m)2m 2 c. n 2 4n 4 d e f. 4m 2 g. 3m 4 n 7 3 h. 2 z 4 i Evaluate each epression for the given value of the variables. a. 2 3 for b. 4 for 3 c for 4 d. 3 2 for 2 and 6. Match epressions from this list that are equivalent but written in different forms. There can be multiple matches. a b. 8 c d e. (2)()()()()() f. (4)2 44 Discovering Algebra More Practice Your Skills 2007 Ke Curriculum Press

4 Lesson 6.4 Scientific Notation for Large Numbers. Write each number in scientific notation. a. 200 b. c. 7 d. 48,900 e. 9,043,000 f. 6,703. g. 3,00 h. 2,00 i. 380 j. 320,000,000 k. 70,000,000,000 l. 8, Write each number in standard notation. a b c d e..8 0 f g h i. 0 6 j k l Use the properties of eponents to rewrite each epression. a. 2 3 () b. 4m 2 3 c d. w3w 8 w 6 e f. z 6 2 g. 6r 3 r 4 3r 2 h i j. 4s 2 t 3 u 4 3 k. m 2 nm 9 n 3 l Write each number in scientific notation. a b c. 2,04 0 d. 800, e f., g. 3, h. 42, i j k l. 89, Find each product and write it in scientific notation without using our calculator. Then set our calculator to scientific notation and check our answers. a b c d A human heart beats about 6 times per minute. B the time ou are 2 ears old, approimatel how man times will our heart have beaten? Epress our answer in scientific notation Ke Curriculum Press Discovering Algebra More Practice Your Skills 4

5 Lesson 6. Looking Back with Eponents. Eliminate factors equivalent to and rewrite the right side of this equation. p 3qr2 pq3 r2 2. Use the properties of eponents to rewrite each epression. 0 a. m m4 b. n 8 c n 8 d m7n4 4 3 e. 9m4n2 f g p p p q q q q q r r p q q q r r h. 2mn7 3m4n2 i. r 2 s r 4s2 3. Lana bought a car 8 ears ago. Since she purchased it, the value of the car has decreased b 2% each ear. The car is now worth about $900. a. Which letter in the equation A( r) could represent the value of the car 8 ears ago when Lana bought it? b. Substitute the other given information into the equation A( r). c. Solve our equation in 3b to find the value of Lana s car when she bought it. 4. Use the properties of eponents to rewrite each epression. a. (3) b c. 4z23 ( 2z) 2 d. 3a 2 b 2 (2ab) 3 e f. r 3 s 6 4rs r4s 8. a. In 2004 Canada had a population of about people. Canada has an area of approimatel square miles. Find the population densit of Canada (the number of people per square mile). b. In 2004 the United States had a population of about people. The United States has an area of approimatel square miles. Find the population densit of the United States. c. How did the population densities of Canada and the United States in 2004 compare? (The World Almanac and Book of Facts 200, p. 848) 46 Discovering Algebra More Practice Your Skills 2007 Ke Curriculum Press

6 Lesson 6.6 Zero and Negative Eponents. Rewrite each epression using onl positive eponents. a. 4 3 b. (7) 2 c. d. 2 4 e. m f. n m 6 n 9 g. 3s 7 w 8 h. 6 z 2 4 7m i. 3 z 2 m 2. Insert the appropriate smbol (,,or) between each pair of numbers. a b c d Find the eponent of 0 that ou need to write each number in scientific notation. a b. 76, c d e. 6,090, f Ms. Frankel has been working for the same compan for ears. She has received a 4.% raise each ear since she started. Her current salar is $42,76. a. Write an epression of the form 42,76( 0.04) for Ms. Frankel s current salar. b. What does the epression 42,76( 0.04) 7 represent in this situation? c. Write and evaluate an epression for her salar ears ago. d. Write epressions without negative eponents that are equivalent to the eponential epressions from 4b and c.. Evaluate each epression without using a calculator. Then check our answers with our calculator. a. 2 b c. (6) 2 d. 0 (2) 3 e f Convert each number to standard notation from scientific notation, or vice versa. a b c d. 969,000,000 e f Ke Curriculum Press Discovering Algebra More Practice Your Skills 47

7 Lesson 6.7 Fitting Eponential Models to Data. Rewrite each value as either r or r.then give the rate of increase or decrease as a percent. a..4 b c d..03 e..2 f. 0. g h.. i Use the equation 240( 0.03) to answer each question. a. Does this equation model an increasing or decreasing pattern? b. What is the rate of increase or decrease? c. What is the -value when is? 3. Use the equation 8( 0.3) to answer each question. a. Does this equation model an increasing or decreasing pattern? b. What is the rate of increase or decrease? c. What is the -value when is 4? 4. Use the equation 902( 0.02) to answer each question. a. Does this equation model an increasing or decreasing pattern? b. What is the rate of increase or decrease? c. What is the -value when is 8?. Write an equation to model the growth of an initial deposit of $00 in a savings account that pas 3.% annual interest. Let B represent the balance in the account, and let t represent the number of ears the mone has been in the account. 6. Write an equation to model the decrease in value of a truck purchased for $26,400 that depreciates b 8% per ear. Let V represent the value of the truck, and let t represent the number of ears since the truck was purchased. 7. Use the properties of eponents to rewrite each epression with onl positive eponents. a. m 6 n7 m8 b. 2 0n2 c d. 2z9 4m4n2 22z04 93z4 e. m3n 2 f z 48 Discovering Algebra More Practice Your Skills 2007 Ke Curriculum Press

8 4. a. b. 3. r represents speed in miles per hour;.r.8(r 6); r 36; 36 mi/h down the river and 30 mi/h up the river 4. n represents ounces of mied nuts, s represents ounces of snack mi n s 8 0.3n 0.0s 0.20(8) n 3.2, s 4.8; 3.2 oz of mied nuts and 4.8 oz of snack mi LESSON.7a Sstems of Inequalities. a. iii b. i c. ii 2. a. No b. No c. Yes d. No e. Yes f. No 3. a. b.. represents shares of Idea Software stock; represents shares of Good Foods stock; , 22; 424 shares of Idea Software and 22 shares of Good Foods 6. t represents time working together in hours; 8 t 6 t ; t ; it will take them about 3 h 26 min to tile the floor together. 7. t represents time working together in hours; 6 (2) 6 t t ; t 9.8, plus the 2 h 9 that Chenani worked alone; it took 3 h, or about 3 h 49 min, to finish all of the donuts. c a. b. c LESSON.7b Miture, Rate, and Work Problems. t represents time driving; 6t 3t 32; t 3.2, or 3 h min 2. represents hours worked in sales; represents hours doing inventor , 20; Frank worked 6 h doing sales and 20 h doing inventor. LESSON 6. Recursive Routines. a. Starting value: 4800; multiplier: 0.2; fifth term: 8.7 b. Starting value: 2; multiplier: 2.; fifth term: c. Starting value: 00; multiplier: 0.9; fifth term: 6.6 d. Starting value: 00; multiplier:.0; fifth term: e. Starting value: ; multiplier: 0.3; fifth term: f. Starting value: 3.; multiplier: 0.; fifth term: a. 2, 8, 27, 40., 60.7 b. 360, 288, 230.4, 84.32, c. 4, 27, 6.2, 9.72,.832 d. 9, 9.8, 43.6, 9.832, e.., 0.7, 0.37, 0.87, a. 6, 24, 36, 4, 8 b. 24,000, 4,800, 960, 92, 38.4 c. 7, 4, 28, 6, 2 d. 40, 88, 93.6, 42.92, e. 00,000, 6,000, 42,20, 27,462., 7, Discovering Algebra More Practice Your Skills / Answers 2007 Ke Curriculum Press

9 4. a. 40( 0.8) b. 0( 0.03) c. W( s) d. 2 2(0.04) e. 3( 0.9) f. 0 0(0.2) g. ( 0.2) h (0.) i. 0,000 0,000(0.0). a. Start with 4, then appl the rule Ans ( 0.0). b. $29.2 c. Februar 0 LESSON 6.2 Eponential Equations. a. (2.) b c. ( 0.07) 3 d a. $70.6 b. $ a. 26,222 b. 27,77 4. a. ii b. iii c. i. a. iv b. iii c. i d. ii 6. represents the emploee s salar, 2,000 represents the emploee s starting salar, represents the number of ears after the emploee was hired, represents 00% of the previous ear s salar, and 0.04 represents an annual 4% raise. 7. a. (2) b. 300(0.4) c. 00(.) LESSON 6.3 Multiplication and Eponents. a. 7w 4 b. 3a 3 b c. p 3 q 2 d. 2 6 e. 36c 4 d 2 f. 8m 4 4m 2. a. (4)(4)(4)(4)(4)(4)(4); 4 7 b. (3)(3)(3)(3)(3)(3)(3); (3) 7 c. (2)(2)(2)(2)(2)(2)(2)(2)(2) (2)(2)(2)(2)(2)(2); (2) d. (8)(8)(8)(8)(8)(8)(8)(8)(8); 8 9 e. ()()()()()()()()()()()()(); 3 f. (n)(n)(n)(n)(n)(n)(n)(n)(n)(n); n 0 3. a. 4 2 b. 8 4 c. 36 d. 30 e. 2 f. (3) 6 g. z 6 h i j k. (6) 20 l. t 4 4. a. 2 2 b. 2m 3 c. 20n 6 d. 3 6 e f. 6m 0 g. 27m 2 n 2 h z 20 i a. 20 b. 40 c. 6 d a, c, and f are equivalent. d and e are equivalent. LESSON 6.4 Scientific Notation for Large Numbers. a b c d e f g h i j k l a. 3,40 b.,200,000 c d. 6,900,000 e. 80,000 f. 6,00 g. 32,000 h. 43,000 i.,000,000 j. 8,000,000,000 k. 40,000,000 l a. 0 4 b. 64m 6 c d. w 9 w 7 e. 6 8 f. 2z 2 g. 6r 7 8r h i j. 64s 6 t 9 u 2 k. m n 4 l a b c d e f g h i j..0 0 k l a b c d About times LESSON 6. Looking Back with Eponents. p 2 q 2 2. a. m 6 b. n 7 c. 3 4 d e. m 3 n 2 f. 2 2 g h. 4mn i. 3r 8 s 3 3. a. A b. 900 A( 0.2) 8 c. About $6, a b. 4 2 c. 6z 4 d. 72a 7 b e f. 4rs 2. a. About 9.26 people per square mile b. About people per square mile c. In 2004, there were about 9 times as man people in the United States per square mile as there were in Canada. LESSON 6.6 Zero and Negative Eponents. a. 4 3 b. ( 7) 2 c. d. 2 4 e. m n f. m6 n9 g. 3 w8 4s 7 h. 6 z2 7m i. 3 m z Ke Curriculum Press Discovering Algebra More Practice Your Skills/Answers 9

10 2. a. b. c. d. 3. a. 4 b. 4 c. d. 7 e. 6 f a. 42,76( 0.04) 0 b. Her salar 7 ears ago c. 42,76( 0.04) 22,000. Fifteen ears ago she earned $22, , 76 42,76 d. ; ( 0. 04) 7 ( 0.04). a. 3 2 b. 6 4 c. 3 6 d. 8 e. f. 6. a. 27,900 b c d e f. 90 LESSON 6.7 Fitting Eponential Models to Data. a. 0.4; rate of increase: 40% b. 0.28; rate of decrease: 28% c. 0.9; rate of decrease: 9% d. 0.03; rate of increase: 3% e. 0.2; rate of increase: 2% f. 0.; rate of decrease: 0% g. 0.0; rate of decrease: % h. 0.; rate of increase: 0% i..2; rate of increase: 2% 2. a. Decreasing b. 3% rate of decrease c a. Decreasing b. 3% rate of decrease c a. Increasing b. 2% rate of decrease c B 00( 0.03) t 6. V 26,400( 0.08) t 8 7. a. m 2 b. 4 n c. 3 d. z 9n 32 e. 2 4 m2 f. 2 3 z LESSON 7. Secret Codes. a. MXSQNDM b. QCGMFUAZ c. EAXHQ 2. a. SOCCER b. RADIO c. EINSTEIN 3. a. Shift each letter up (right) b 8 letters. Here is the coding grid. Coded output b. TOP SECRET 4. a. All the letters of the alphabet b. All the letters of the alphabet c. Yes. Each input has a unique output. LESSON 7.2 Functions and Graphs. a. Input Output b. c. X YZ U V W R ST Q O P N M K L H IJ G D EF A B C Input Output ABCDEFGHI J KLMNOPQRSTUVWXYZ Original input Input Output Discovering Algebra More Practice Your Skills / Answers 2007 Ke Curriculum Press