MATH 1020 TEST 2 VERSION A Fall Printed Name: Section #: Instructor:

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1 Printed Name: Section #: Instructor: Please do not ask questions during this exam. 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 last page of the test for formulas, general directions, and calculator troubleshooting tips. Any communication with any person (other than the instructor or the designated proctor) during this exam 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 #1AB FR #1CD FR # FR #3 FR #4 scantron Free Response Total Multiple Choice Total Total Possible Points Points Earned Useful Formulas: ( ) f x+ h f( x) f ( x) = lim ; h 0 h f( x) f( a) f ( a) = lim x a x a rt r Ft () = P(1 + rt) Ft () = Pe Ft () = P 1+ n r r APY = ( e 1)100% or APY = % n n ( nt) Page 1/1

2 MULTIPLE CHOICE: 57 points (3 points each, unless otherwise noted) Use a # 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. 1. Consider the following two interest options. I: compounds interest semi-annually at.50% II: compounds interest continuously at.49% The annual percentage yield (APY) for option I is % and the APY for option II is %. a..500,.490 b..516,.51 c..56,.519 d..53,.5 Use the information for the following two questions: Sherri decided to place $65 in a new bank account that pays.40 % interest compounded quarterly.. If there are no further deposits or withdrawals, what is the future value of Sherri s account after months? a. $ b. $ c. $ d. $ If there are no further deposits or withdrawals, how long will it take Sherri s money to double? a. 9 years 0 months b. 8 years 10 months c. 8 years 6 months d. 8 years 9 months 3 3x x 4. Find the derivative of f( x) =. f ( x) =. x a. 3 4x b. 6x 3x c. 3 x d. 3 1 x x Page /1

3 5. gx ( ) 1 x =. 3 = + x has derivative g ( x) a. 1 3 x + x b. 1 3 x + x c x + x d. 3 3 x + x 1 6. To find the instantaneous rate of change at a point x = for an everywhere differentiable function f( x ) using the numeric method,. a. find the slopes of secant lines between x = and nearby points and take the limit of the secant slopes, as the nearby points approach x = b. find the slopes of secant lines between x = and nearby points and take the average of the secant slopes c. find the derivative at points close to x = and take the limit of the derivatives, as the nearby points approach x = d. find the derivative at points close to x = and take the average of the derivatives 7. For an everywhere differentiable function f( x ), a. slope of the tangent line at the input value of h lim h 0 f( x+ h) f( x) h describes the. b. slope of the secant lines between the input value of x and nearby points x+ h c. slope of the secant line at the input value of x d. slope of the tangent line at the input value of x Use the following to answer the next two questions. In 016, Walt Disney Company s revenue from its parks and resorts segment worldwide was billion dollars and revenue was increasing by billion dollars per year. 8. Find the percentage rate of change in Disney s parks and resorts worldwide revenue in 016. a b c d [ pts] What are the units on the percentage rate of change? a. billion dollars per year b. percent per dollar c. percent per year d. percent Page 3/1

4 Use the following to answer the next two questions. The table below shows the per capita consumption of caloric sweeteners in the US for various years. Year Per capita consumption, in pounds Find the percent change in per capita consumption of caloric sweeteners in the US between 006 and 015. a % b % c % d % 11. Find the average rate of change in per capita consumption of caloric sweeteners in the US between 006 and 015. a pounds per year b pounds per year c pounds per year d pounds per year 1. Which one of the following graphs shows a correctly drawn tangent line at the inflection point P? a. b. c. d. Page 4/1

5 13. Which one of the following could be a graph of f( x ) if f ( 1) = 0, f (0) = 0.6, and f (1) = 0? a. b. c. d. 14. Which one of the following graphs is the slope graph for the function f( x) shown in the graph below? a. b. c. d. Page 5/1

6 15. Which one of the following is the slope graph for the function f( x ) shown in the graph below? a. b. c. d. 16. [ pts] Consider the three points A, B, and P on the graph to the right. Order the three points from least to greatest SLOPE. a. B, A, P b. A, B, P c. P, B, A d. P, A, B 17. Consider the graph of f( x) shown to the right. Identify the input value(s) for which the function is continuous, but its derivative does not exist. a. x = 1, x = 3, and x = 5 b. x = 5 only c. x = 1 and x = 3 only d. x = 1 and x = 5 only Page 6/1

7 Use the graph of f( x) shown below to answer the following four questions about the slope graph f ( x). [ pts each] 18. On the interval (,10), the slope graph of f( x ). a. lies completely below the x-axis b. lies completely above the x-axis c. has exactly one x-intercept d. has one inflection point 19. At the inflection point x = 1.35, the slope graph of f( x ) has. a. a relative maximum b. a relative minimum c. an inflection point d. a zero 0. On the interval (,10), the slope graph of f( x ) is increasing on the interval. a. (,10) b. (,1.35) c. (1.35,10) d. nowhere 1. At the point x = 10, the slope graph of f( x) will display. a. a vertical asymptote b. two closed circles c. one open circle and one closed circle d. two open circles Page 7/1

8 FREE RESPONSE: 43 points Show work where possible. Read the directions at the back of the test on rounding, inclusion of units, and writing sentences and models Bx ( ) = 0.006x 0.135x x+.7 million barrels gives the annual craft beer production in the US, x years after 1994, 0 x 19. check point: B () = A. Find and interpret the average rate of change between the points x = 3 and x = 13. B. Fill in the table to numerically estimate B (14). Each entry should be rounded to exactly FOUR decimal places for full credit. (Always show the fourth decimal place, even in the case that it is a zero.) x 14 Bx ( ) B(14) x x 14 Bx ( ) B(14) x 14 B (14) = (rounded to four decimal places) ( 1A -1B /1.5 pts ) THIS PROBLEM, WITH THE SAME MODEL, CONTINUES ON THE NEXT PAGE Page 8/1

9 Bx = x x + x+ million barrels gives the annual craft beer production in the US, 3 ( ) x years after 1994, 0 x 19. check point: B () = C. Write a sentence of interpretation for db = dx = x 9 D. Give a completely defined rate-of-change model for Bx ( ) by filling in the blanks. B ( x) = (equation) (units) gives the, x years after 1994, 0 x 19. ( 1C -1D / 9 pts ). Find the derivative of f( x) = π x e +. Use proper notation for full credit. x 1 ( / 3.5pts ) Page 9/1

10 3. The following graph shows the total number of downloads, in thousands, of the single #selfie by the band The Chainsmokers, x weeks after its initial release on January 9, 014. Complete each of the following sentences with the correct numeric value, correctly rounded to three decimal places. For full credit, show work when needed. A. Nine weeks after the initial release of the single #selfie, the total number of downloads was thousand downloads. B. Nine weeks after the initial release of the single #selfie, the total number of downloads was increasing by thousand downloads per week. C. Between six and nine weeks after the initial release of the single #selfie, the total number of downloads increased on average by thousand downloads per week. D. Between six and nine weeks after the initial release of the single #selfie, the total number of downloads increased by %. ( / 8pts ) Page 10/1

11 4. Use the limit definition of the derivative to find the derivative of f( x) = 4x 1.5x+ 6. For full credit, continue from the general limit definition (provided below), clearly showing all necessary algebraic steps (cancellations, expansions, etc.) and including proper use of notation and equal signs. f ( x) = lim h 0 f( x+ h) f( x) h = ( / 9 pts ) 1 point for correctly filling out and bubbling the scantron with a # pencil, a correct XID, a correct test version AND the front of the test is completed with your signature on the academic integrity statement. END OF TEST Page 11/1

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 context 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 context 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, L, 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 L. ZOOM 0 may not work for graphing if Plot 1 is turned on. DIM MISMATCH error usually means that the lists in L1 and L 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 extra 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 x in Y1. If you need to CLEAR MEMORY, use nd +, 7:Reset, 1:All Ram, :Reset Page 1/1