Printed Name: Section #: Instructor:

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1 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 the net page for 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+, 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 FR#5 Scantron Free Response Total Multiple Choice Total Total Possible Points Points Earned Page 1/11

2 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. MATH SOLVER only works if there is a variable in Y1. Page 2/11 If you need to CLEAR MEMORY, use 2 nd +, 7:Reset, 1:All Ram, 2:Reset

3 MULTIPLE CHOICE: 62 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. B A C B D C B B D A C B D C D A C D B C A D D A Use the following information to answer the net three questions. st ( ) = t billion dollars gives the amount of student debt in the US, t years since 2004, 0 t For the model above, state the input description ; and input units of measure. a. billion dollars; years b. number of years since 2004; years c. years; billion dollars d. amount of student debt in the US; billion dollars 2. Use the above model to complete the following sentence of interpretation for the slope: Between 2004 and 2016, the amount of student debt in the US increased by. a billion dollars per year b billion dollars c billion dollars per year d billion dollars 3. Write the following using function notation: In 2014, the amount of student debt in the US was 1, billion dollars. a. s (14) = 1,142, 269,000,000 b. s (14) = 1, c. s (10) = 1, d. s (10) = 1,142, 269,000, In 1995, the population of Russia was million people. Between 1995 and 2005, Russia s population decreased by 0.5 percent each year. Use the given information to complete the model: R ( ) = million people gives the population of Russia, years since 1995, a b (0.995 ) c (1.005 ) d Page 3/11

4 5. The birth rate in Japan can be modeled by J( ) = ( ) births for every thousand people, years after 1970, The constant percentage change for J( ) is. a % b. 97.6% c % d. -2.4% 6. The table below shows craft beer production in the US for various years. Align the input data to the number of years after Using the scatter plot, find the best fitting function to model the aligned data and write a completely defined model. Year Number of barrels, in millions a. B ( ) = 2.690(1.092 ) million barrels gives the yearly craft beer production in the US, years after 1994, b. c. d. B = + million barrels gives the yearly craft 3 2 ( ) , ,950, beer production in the US, in year, B ( ) = million barrels gives the yearly craft beer production in the US, years after 1994, B ( ) = 6.854(10 )(1.092 ) million barrels gives the yearly craft beer production in the US, in year, R ( ) million people gives the number of refugees worldwide, in year, S ( ) million people gives the number of refugees who are from Syria, in year, Find a meaningful new function p ( ) that describes the percentage of the total number of refugees worldwide who are from Syria in year. a. R ( ) S ( ) p ( ) = b. 100 S ( ) p ( ) = 100 R ( ) c. R ( ) S ( ) p ( ) = d. p ( ) = 100 RS ( ( )) 100 Page 4/11

5 Use the following information to answer the net two questions. [2 pts each] st () thousand dollars gives the average student debt of a graduating college senior in the US, t years since hs () months is the average amount of time it takes to pay off an average student debt of s thousand dollars. 8. Find a new meaningful function that can be constructed from the given models. a. st () hs () b. hst ( ( )) c. hs () st () d. sht ( ( )) 9. The new meaningful function constructed from the given models has input units and output units. a. thousand dollars, years per month b. years, thousand dollars per year c. thousand dollars, months d. years, months Use the following information to answer the net two questions. [2 pts each] An automobile dealership sells N( ) hundred Toyota Scion cars yearly when the price of its base model is thousand dollars per car, What is the dealership s yearly revenue R ( ) from the sale of the Toyota Scion base model? a. R ( ) = N ( ) b. R ( ) = + N ( ) c. R ( ) = d. R ( ) = N( ) 11. What are the output units for the yearly revenue R ( ) from the sale of the Toyota Scion base model? a. thousand dollars per car b. thousand dollars c. hundred thousand dollars d. hundred cars per thousand dollars Page 5/11

6 12. When interchanging the input and output values of an eponential growth function, the resulting inverse function is. a. an eponential decay function b. logarithmic c. logistic d. cubic 13. Which one of the following limits is suggested by the table? a. lim g( ) = 0 0 b. lim g( ) = c. lim g( ) = - 0 d. lim g( ) = 0 g ( ) , , , A student club is planning a fund raiser formal dinner-dance. The club has projected the following total costs and revenue. C ( ) = dollars is the cost associated with the production of the formal dinner- dance, when tickets are sold, R ( ) = 50 dollars is the revenue from the sale of tickets to the formal dinner-dance, How many tickets must be sold so that the student club will break-even? a. 20 b. 30 c. 50 d. 100 Page 6/11

7 Use the following graph of the function f( ) to answer the net five questions. [2 pts each] 15. lim 1 f( ) = a. 5 b. 5 c. d. 16. lim f( ) = a. 5 b. 5 c. d. 17. The equation of the horizontal asymptote to the graph of f( ) is. a. = 1 b. = 5 c. y = 5 d. y = The graph of f( ) is increasing on the interval(s). a. (,1) only b. (1, ) only c. (,1) and (1, ) d. nowhere 19. The graph of f( ) is concave up on the interval(s). a. (,1) only b. (1, ) only c. (,1) and (1, ) d. nowhere Page 7/11

8 20. Complete the following for the function f( ) = ln( ). lim f ( ) = and f( ). a. ; has two asymptotes b. zero; has two asymptotes c. ; has one asymptote d. zero; has one asymptote 21. Which one of the following statements regarding the function f( ) = e is FALSE? a. y = is a horizontal asymptote. b. lim f( ) = c. The function is decreasing. d. y = 0 is a horizontal asymptote. 22. Which one of the following functions has a graph with lim f( ) =? a. f( ) = a(2 ), a = 5 b. c. f ( ) = a + b, a = 3 d. 2 f ( ) a b c = + +, a = f ( ) a b c d = + + +, a = [2 pts] Which one of the following relations does NOT satisfy the definition of a function, given is the input variable and y is the output variable? a. 1 y = e b. y = 5 1 c. + y 2 = d. = The graphs below are two eamples of a(n) function. a. logarithmic b. eponential c. quadratic d. logistic Page 8/11

9 FREE RESPONSE: 38 points Show work where possible. Read the directions at the front of the test on rounding, inclusion of units, and writing models and sentences S ( ) = million people gives the number of registered Skype users, years since (the end of) 2004, 0 3. Checkpoint: S ( 3) = a. Find S ( ) when = 2. Write a sentence of interpretation S (2) = In 2006, the number of registered Skype users was million people. Part a) 5 pts Part b) 1 pt Part c) 3 pts b. Part (a) uses interpolation/ etrapolation (circle one). c. Use the model to complete the following sentence: If the trend indicated by the model continued, the number of Skype users was projected to reach 428,000,000 people years after (the end of) 2004, in the year (round answer to 3 decimal places) (specify the year) S ( ) = 428 = In each of the following, circle all function types having ( / 9 pts ) 1 pt for each correctly circled function a. eactly one concavity. linear eponential logarithmic logistic quadratic cubic b. eactly one inflection point. linear eponential logarithmic logistic quadratic cubic c. no concavity. linear eponential logarithmic logistic quadratic cubic d. a constant percentage change. linear eponential logarithmic logistic quadratic cubic ( / 7 pts ) Page 9/11

10 3. Use the graph of function f( ) below to answer the following questions. Part a) 4 pts Part b) 2 pts Part c) 2 pts Part d) 1 pt a. Fill in the blanks. A limit must specify a number,,, or DNE (if the answer does not eist or is undefined). lim f( ) = 4 lim f( ) = 4 lim f ( ) = 4 2 f (2) = 8 b. Which one of the four statements below is TRUE? Circle the correct sentence. The function f( ) is continuous at = 2. The function f( ) is not continuous at = 2 because f (2) The function f( ) is not continuous at = 2 because The function f( ) is not continuous at = 2 because 2 is undefined. lim f( ) does not eist. f (2) lim f( ) c. Fill in the blanks. A limit must specify a number L,,, or DNE (if the answer does not eist or is undefined). 2 lim f( ) = - lim f( ) = - d. Consider the portion of the graph of f( ) on the interval 2< < 2. How many inflection points are there? Circle the answer. Zero inflection points on 2< < 2 One inflection point on 2< < 2 Two inflection points on 2< < 2 Three inflection points on 2< < 2 ( / 9 pts ) Page 10/11

11 4. For a ride with UberSelect in Los Angeles, Uber charges a flat fee of $5.00 and $2.35 for each mile traveled. Find an equation that completes the model: U( ) = dollars gives the fare for a ride of miles with UberSelect in Los Angeles, > 0. 3 pts for correct equation ( / 3pts ) 5. A band called The Chainsmokers released a single called #selfie on January 29, The table below shows the total number of downloads, in thousands, of the single #selfie for various weeks since the single was released. Weeks since release Number of Downloads, in thousands a. Look at scatter plot of the data. How many concavities are suggested by the scatter plot of the data? Circle one: Part a) 1 pt b. Find a logistic function to model the data and write a completely defined model f( ) = thousand downloads is the total number of e downloads of the single #selfie by the band The Chainsmokers, weeks since its initial release January 29, 2014, Part b) 4 pts function equation 1 pt output units 1 pt output description 1.5 pt input units and description 0.5 pts input data range ( / 9 pts ) 6. 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 11/11