Printed Name: Section #: Instructor:

Printed Name: Section #: Instructor: Please do not ask questions during this eam. If you consider a question to be ambiguous, state your assumptions in the margin and do the best you can to provide the correct answer. Refer to this page and the net for formulas, general directions, and calculator troubleshooting tips. Any communication with any person (other than the instructor or the designated proctor) during this eam in any form, including written, signed, verbal or digital, is understood to be a violation of academic integrity. All devices, such as computers, cell phones, cameras, watches and PDAs must be turned off and stowed away while the student is in the testing room. The only calculators to be used are TI-83, TI-83+, TI-84 or TI-84+. You may NOT borrow or share a calculator with another person taking this test. Statement of Academic Integrity: I have not and will not give or receive improper aid on this test. In signing below, I acknowledge that I have read, understand, and agree to these testing conditions. Student s Signature: (This test will not be accepted for grading unless it bears the signature of the student.) FR#1 FR #2 FR #3 FR #4 scantron Free Response Total Multiple Choice Total Total Possible Points 10 12 10 4 1 37 63 100 Points Earned Page 1/12

General Directions: Show work where possible. Answers without supporting work (where work is appropriate) may receive little credit. Do not round intermediate calculations. Answers in contet ALWAYS require units. Assume end of the year data unless stated otherwise. Round your answers to 3 decimal places UNLESS the answer needs to be rounded differently to make sense in the contet of the problem OR the directions specify another type rounding OR the complete answer has fewer than 3 decimal places. When asked to write a model, include all components of a model: an equation, a description of the input including units, a description of the output including units, and the input interval when known. When asked to write a sentence of practical interpretation, answer the questions: when?, what?, and how much? using ordinary, conversational language. DO NOT use math words, terms, or unnecessary phrases. Always use a ruler when estimating values off of a graph. HINTS FOR TROUBLESHOOTING YOUR CALCULATOR: If you lose your L1, L2, etc., you may reinsert them using STAT 5 (set-up editor) enter. The SCATTER PLOT will not show unless Plot 1 has been turned on and there is data in L1 and L2. ZOOM 0 may not work for graphing if Plot 1 is turned on. DIM MISMATCH error usually means that the lists in L1 and L2 are not of equal length. DATA TYPE error usually means that you already have something in Y1 and you need to clear it before you can paste a new equation. INVALID DIM error usually means that your plot(s) are on, but that you have no data in the lists. Refer to the second hint above. If your batteries die, raise your hand and hold up your calculator. If your instructor has an etra calculator available, he/she will loan it to you for a few minutes. SYNTAX ERROR: Try GO TO. This will happen if you use a subtraction minus sign when you should use a negative sign. If you need to CLEAR MEMORY, use 2 nd +, 7:Reset, 1:All Ram, 2:Reset Page 2/12

MULTIPLE CHOICE: 63 points Use a #2 pencil and completely fill each bubble on your scantron to answer each multiple choice question. (For future reference, circle your answers on this test paper.) There is no penalty for guessing on multiple choice. If you indicate more than one answer, or you leave a blank, the question will be marked as incorrect. Each question is worth 3 points, unless otherwise indicated. D B C D A B B C C B A C D D C D B A B C A D A 1. [2 pts] A student s raw score on a spelling test with twenty evenly weighted questions can be epressed by g( n) = 5n when she spells n words correctly. The function g has a(an) representation. a. numerical b. verbal c. graphical d. algebraic 2. [2 pts] Which one of the following relations is NOT function? a. b. c. d. 3. r( t) = 1.2 t + 17 thousand dollars gives the resale value of a new car, t years after its purchase, 0 t 10. Complete the following sentence of interpretation for the slope of r( t ). During the 10 year period after the car was first purchased, its resale value. a. increased by 17 thousand dollars per year b. decreased by 1.2 thousand dollars c. decreased by 1.2 thousand dollars per year d. increased by 17 thousand dollars 4. [2 pts] Which one of the following best describes a linear function? a. Concavity on linear functions varies, but linear functions have a constant rate of change. b. Concavity on linear functions varies, but linear functions have a constant percentage change. c. Linear functions have no concavity and have a constant percentage change. d. Linear functions have no concavity and have a constant rate of change. Page 3/12

5. [2 pts] A company that manufactures both skateboards and wrist-braces analyzed their national sales data and found a correlation between the number of skateboards sold and the number of wrist-braces sold. w( s ) thousand wrist-braces gives the number of wrist-braces sold when s hundred skateboards were sold, 0 s 52. Identify the input and output units: a. input units: hundred skateboards; output units: thousand wrist-braces b. input units: thousand wrist-braces; output units: hundred skateboards c. input units: number of wrist-braces sold; output units: number of skateboards sold d. input units: number of skateboards sold; output units: number of wrist-braces sold 6. The International Monetary Fund created a three-year forecast of Spain s budget deficit, starting with a deficit of 6.2 percent in 2012, with a projected annual decrease in its budget deficit of 25% each year. S( = ) 2012, 0 3. percent gives the value of Spain s budget deficit, years after a. 6.2(0.25 ) b. 6.2(0.75 ) c. 6.2(1.25 ) d. 25(0.9938 ) 7. H ( t ) = 213(0.42) t million dollars gives a business s total profit, where t is the number of years since 1989, 0 t 12. Find the constant percent change for this model to fill in the blanks: Between 1989 and 2001, a business s total profit each year by percent. a. increased; 1.42 b. decreased; 58 c. decreased; 42 d. increased; 213 8. In 2010, yellow cabs in New York City averaged 463.701 thousand daily trips, and saw a decrease of 4.2 thousand daily trips each year between 2010 and 2016. Find a model by filling in the blank: thousand daily trips gives the average number of daily trips by yellow cabs in NYC, t years since 2010, 0 t 6. a. d( t ) = 463.701(1.042 t ) b. d( t) = 463.701 t 4.2 c. d( t) = 4.2 t + 463.701 d. d( t ) = 463.701(0.958 t ) Page 4/12

Use this information for the net two questions: A US toy company, with a European branch, sells novelty fidget spinners. P( c ) euros gives the toy company s profit in euros when c hundred novelty fidget spinners are sold. D( p ) dollars gives the equivalent dollar amount of p euros. 9. [2 pts] Produce a function that gives the toy company s profit from the sale of novelty fidget spinners, in dollars. a. P( D ) b. P( c) D( p) c. D( P( c )) d. P( c) D( p) 2 10. [2 pts] If P( c) = c ln( c) and D( p) = 1.19 p, find the profit in dollars when 7.45 hundred fidget spinners are sold: a. 76.41 dollars b. 63.66 dollars c. 53.49 dollars d. 474.25 dollars Use the following to answer the net two questions. S( p) = 1.075p + 11.775 thousand gallons represents daily sales of MOO brand of milk, when the price of one gallon is p dollars per gallon, 1 p 5. 11. Find the daily revenue R( p ) = generated from sales of MOO brand of milk. a. ( p)( 1.075 p + 11.775) b. 1.075p + 11.775 p c. 1.075p + 11.775 d. ( 1.075 p + 11.775) p 12. What are the output units for the daily revenue R( p )? a. dollars per thousand gallons b. thousand gallons c. thousand dollars d. thousand dollars per gallon Page 5/12

13. A biologist has decided to study the growth of Staphylococcus bacteria. The table below gives the number of Staph bacteria present in a petri dish, t hours after the eperiment began, 1 t 4. Time, in hours 1 2 3 4 Amount of bacteria present 100 395 1602 6395 Create an inverse function and write a logarithmic function to complete the model for that inverse function. f ( ) = hours gives the amount of time it that has passed since the beginning of the eperiment, when there are Staph bacteria in the petri dish. a. 24.853(4.005 ) c. 1.569(1.0002 ) b. 919.693 + (3829.631) ln( ) d. 2.316 + (0.721) ln( ) 14. Let f ( ) = 3+ 0.5ln( ). Which one of the following statements is true? a. f is increasing and concave up. b. f is decreasing and concave down. c. f is decreasing and concave up. d. f is increasing and concave down. 15. Let f ( ) = 5 2ln( ). Which one of the following statements is false? a. f has a vertical asymptote at = 0. b. f is a decreasing function. c. f has a horizontal asymptote at y= 0. d. lim f ( ) =. + 0 16. Find the one statement below that correctly describes the behavior for the function 2 f ( ) = 2.5 4.83 39.442. a. There is an inflection point on the graph of f. b. The graph of f is concave down everywhere and has a maimum value. c. The graph of f is concave up everywhere with a maimum value. d. lim f ( ) = and lim f ( ) = Page 6/12

Use the following graph to answer the net two questions. 17. On what interval is the above graph concave down? a. (,1.82) b. (, 1) c. ( 3.75, 1.82) d. ( 1, ) 18. On what interval is the above graph increasing? a. (, 3.75),(1.82, ) b. ( 3.75,1.82) c. ( 1, ) d. (1.82, ) only 19. Use the tables below to numerically estimate the end behavior of an eponential function f ( ). a. lim f ( ) = ; lim f ( ) = b. lim f ( ) = 0 ; lim f ( ) = c. lim f ( ) = ; lim f ( ) = d. lim f ( ) = 0 ; lim f ( ) = 0 f() -10 0.971-100 0.741-1,000 0.050-10,000 14 9.787 (10 ) f() 100 1.349 1,000 19.996 5,000 3,196,429.294 10,000 13 1.022 (10 ) Page 7/12

Use the graph of the function f ( ) below to answer the net two questions. 20. The function above is at = 2 because. a. continuous; lim f ( ) 2 eists b. not continuous; f ( 2) is undefined c. not continuous; lim f ( ) does not eist 2 d. continuous; lim f ( ) = f ( 2) 2 21. Which one of the following statements is false for the above function? a. lim f ( ) = 4 b. lim f ( ) = + 4 c. lim f ( ) lim f ( ) d. + 4 4 lim f ( ) = 4 56 22. After filling in the table below, it is appears that f ( ) = 2 6 has a asymptote given by the equation. Check point: f (2) = 7 a. vertical; = 93,332 b. horizontal; y= 6 c. horizontal; y= 93, 332 d. vertical; = 6 f ( ) 6.1 6.01 6.001 6.0001 6.00001 Page 8/12

23. Consider functions with two concavities. A function may have a relative maimum and a relative minimum but has no horizontal asymptotes, and a function has two horizontal asymptotes. a. cubic; logistic b. quadratic; cubic c. logistic; cubic d. quadratic; logarithmic FREE RESPONSE: 37 points Show work where possible. Read the directions at the front of the test on rounding, inclusion of units, and writing models and sentences. 1. The table below gives the average life epectancy of Americans in various years. Year 1920 1930 1940 1950 1960 1970 Average Life Epectancy, in years 54.1 59.7 63.8 66.9 69.4 71.5 a. View the scatterplot and circle the number of concavities: zero / one / two concavities Part a) 2 pts Part b) 4.5 pts function equation 1 pt output units 1 pt output description 1 pt input units and description 1/2 pt input data range b. Align the data to the number of years since 1900. Find a logarithmic function to model the data and write a completely defined model for average life epectancy. L( ) = 12.391+ 13.923ln years (of age) gives the average life epectancy of American, years after 1900, 20 70. ( /10 pts ) Page 9/12

2. The distance a vehicle will travel while braking to come to a complete stop is related to its initial speed. 2 D( ) = 0.048 + 2.206+ 0.262 feet gives the stopping distance for a vehicle traveling at miles per hour, 10 90. Checkpoint: D (2) = 4.866 Part a) 2 pts Part b) 2 pts Part c) 3 pts Part d) 2 pts Part e) 3 pts a. Find D( ) when = 55. 266.792 b. Write the answer to part a) in function notation. D (55) = 266.792 c. Write the answer to part a) and part b) in a sentence of interpretation. When a vehicle is traveling at 55 miles per hour, its stopping distance is 266.792 feet. d. Does the answer to part a) use interpolation or etrapolation? _interpolation e. At what speed would a vehicle be traveling if it took 50.5 feet for it to stop? Round the answer to 3 decimal places and include units. 16.703 mph ( /12 pts ) Test continues on net page Page 10/12

2450.736 3. Consider the function: V ( t) = 0.885t 1 + 337.238e. Check point: V (2) 41.934 a. Circle the appropriate answer or fill in the blank for each of the following. i) V ( t ) has zero / one / two concavities. Part a) 7 pts ii) V ( t ) is an increasing / decreasing function. iii) lim V ( t) = 0 t iv) lim V ( t) = 2450.736 t v) Name all the vertical and/or horizontal asymptotes by writing their equations. If none, write none. Vertical: none Horizontal: y= 0, y= 2450.736 b. The cumulative number of visitors to an all-year-round amusement park is described in the following 2450.736 model. V ( t) = 0.885t 1 + 337.238e thousand visitors gives the cumulative number of visitors to an amusement park, at the end of month t ( t= 1is January, etc.), 1 t 12. In what month will the cumulative number of visitors reach one million (hint: one million = 1000 thousands)? Give the answer rounded to 3 decimal places and then give the month in which this will occur by filling in the blanks: Part b) 3 pts The cumulative number of visitors to an amusement park reaches one million in _6.157 months, which is in July (name the month). ( /10 pts ) 4. A company selling computers reports that C( t) billion dollars are its total costs and P( t) billion dollars gives its profits during the th t quarter. Complete the model for the revenue R( t ) by filling in the blanks with the equation and its output units: R( t) = P( t+ ) C( t) billion dollars gives the revenue for a (equation) company selling computers, during the (units) 2 pts per blank th t quarter. ( / 4 pts) Page 11/12

5. A scantron correctly bubbled with a #2 pencil, a correctly-bubbled XID, a correctly-bubbled test version, AND a signed academic integrity statement (on the front of the test) earns 1 point. END OF TEST Page 12/12