Printed Name: Section #: Instructor:

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1 Printed Name: Section #: Instructor: Please do not ask questions during tis exam. If you consider a question to be ambiguous, state your assumptions in te margin and do te best you can to provide te correct answer. Refer to tis page and te last page of te test for formulas, general directions, and calculator troublesooting tips. Any communication wit any person (oter tan te instructor or te designated proctor) during tis exam in any form, including written, signed, verbal or digital, is understood to be a violation of academic integrity. All devices, suc as computers, cell pones, cameras, watces and PDAs must be turned off and stowed away wile te student is in te testing room. Te only calculators to be used are TI-83, TI-83+, TI-84 or TI-84+. You may NOT borrow or sare a calculator wit anoter person taking tis test. Statement of Academic Integrity: I ave not and will not give or receive improper aid on tis test. In signing below, I acknowledge tat I ave read, understand, and agree to tese testing conditions. Student s Signature: (Tis test will not be accepted for grading unless it bears te signature of te student.) FR #1AB FR #1CD FR # FR #3 FR #4 scantron Free Response Total Multiple Coice Total Total Possible Points Points Earned Useful Formulas: ( ) f x+ f( x) f ( x) = lim ; 0 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 eac, unless oterwise noted) Use a # pencil and completely fill eac bubble on your scantron to answer eac multiple coice question. (For future reference, circle your answers on tis test paper.) Tere is no penalty for guessing on multiple coice. If you indicate more tan one answer, or you leave a blank, te question will be marked as incorrect. B C A C B A D B C A D D C B A C D A B C D 1. Consider te following two interest options. I: compounds interest semi-annually at.50% II: compounds interest continuously at.49% Te annual percentage yield (APY) for option I is % and te APY for option II is %. a..500,.490 b..516,.51 c..56,.519 d..53,.5 Use te information for te following two questions: Serri decided to place $65 in a new bank account tat pays.40 % interest compounded quarterly.. If tere are no furter deposits or witdrawals, wat is te future value of Serri s account after monts? a. $ b. $ c. $ d. $ If tere are no furter deposits or witdrawals, ow long will it take Serri s money to double? a. 9 years 0 monts b. 8 years 10 monts c. 8 years 6 monts d. 8 years 9 monts 4. Find te derivative of 3 3x x 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 as 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 te instantaneous rate of cange at a point x = for an everywere differentiable function f( x ) using te numeric metod,. a. find te slopes of secant lines between x = and nearby points and take te limit of te secant slopes, as te nearby points approac x = b. find te slopes of secant lines between x = and nearby points and take te average of te secant slopes c. find te derivative at points close to x = and take te limit of te derivatives, as te nearby points approac x = d. find te derivative at points close to x = and take te average of te derivatives 7. For an everywere differentiable function f( x ), a. slope of te tangent line at te input value of lim 0 f( x+ ) f( x) describes te. b. slope of te secant lines between te input value of x and nearby points x+ c. slope of te secant line at te input value of x d. slope of te tangent line at te input value of x Use te following to answer te 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 te percentage rate of cange in Disney s parks and resorts worldwide revenue in 016. a b c d [ pts] Wat are te units for te percentage rate of cange? a. billion dollars per year b. percent per dollar c. percent per year d. percent Page 3/1

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

5 13. Wic one of te following could be a grap of f( x ) if f ( 1) = 0, f (0) = 0.6, and f (1) = 0? a. b. c. d. 14. Wic one of te following graps is te slope grap for te function f( x) sown in te grap below? a. b. c. d. Page 5/1

6 15. Wic one of te following is te slope grap for te function f( x ) sown in te grap below? a. b. c. d. 16. [ pts] Consider te tree points A, B, and P on te grap to te rigt. Order te tree points from least to greatest SLOPE. a. B, A, P b. A, B, P c. P, B, A d. P, A, B 17. Consider te grap of f( x) sown to te rigt. Identify te input value(s) for wic te 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 te grap of f( x) sown below to answer te following four questions about te slope grap f ( x). [ pts eac] 18. On te interval (,10), te slope grap of f( x ). a. lies completely below te x-axis b. lies completely above te x-axis c. as exactly one x-intercept d. as one inflection point 19. At te inflection point x = 1.35, te slope grap of f( x ) as. a. a relative maximum b. a relative minimum c. an inflection point d. a zero 0. On te interval (,10), te slope grap of f( x ) is increasing on te interval. a. (,10) b. (,1.35) c. (1.35,10) d. nowere 1. At te point x = 10, te slope grap 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 Sow work were possible. Read te directions at te back of te test on rounding, inclusion of units, and writing sentences and models Bx ( ) = 0.006x 0.135x x+.7 million barrels gives te annual craft beer production in te US, x years after 1994, 0 x 19. ceck point: B () = A. Find and interpret te average rate of cange between te points x = 3 and x = 13. B(13) B(3) = Between 1997 and 007, annual craft beer production in te US increased on average by million barrels per year. Part A) 6.5 pts ½ pt wen, 1 pt wat, 1 pt increased, 1 pt on average by pts ow muc, 1 pt units B. Fill in te table to numerically estimate B (14). Eac entry sould be rounded to exactly FOUR decimal places for full credit. (Always sow te fourt decimal place, even in te case tat it is a zero.) x 14 Bx ( ) B(14) x 14 + x 14 Bx ( ) B(14) x B (14) = (rounded to four decimal places) Part B) 5 pts entries in table, correct to four decimal places 1 pt derivative THIS PROBLEM, WITH THE SAME MODEL, CONTINUES ON THE NEXT PAGE ( 1A -1B /1.5 pts ) Page 8/1

9 3 Bx ( ) = 0.006x 0.135x x+.7 million barrels gives te annual craft beer production in te US, x years after 1994, 0 x 19. ceck point: B () = C. Write a sentence of interpretation for db = dx = In 003, annual craft beer production in te US was increasing by million barrels per year. x 9 Part C) 4 pts ½ pt wen, 1 pt wat, 1 pt was increasing by, ½ pt ow muc, 1 pt units D. Give a completely defined rate-of-cange model for Bx ( ) by filling in te blanks. B x = + million barrels per year ( ) 0.018x 0.70x (equation) (units) gives te _ rate of cange in annual craft beer production in te US _, x years after 1994, 0 x 19. Part D) 5 pts pts derivative 1 pt units 1 pt rate of cange 1 pt output description ( 1C -1D / 9 pts ). Find te derivative of f( x) = π x e +. Use proper notation for full credit. x 1 1 f( x) = π x e + x 1 1 f ( x) = π 0 x = π x pts notation 3 pts derivative ( / 3.5 pts ) Page 9/1

10 3. Te following grap sows te total number of downloads, in tousands, of te single #selfie by te band Te Cainsmokers, x weeks after its initial release on January 9, 014. Complete eac of te following sentences wit te correct numeric value, correctly rounded to tree decimal places. For full credit, sow work wen needed. pts eac part A. Nine weeks after te initial release of te single #selfie, te total number of downloads was 80.5 tousand downloads. (9,80.5) B. Nine weeks after te initial release of te single #selfie, te total number of downloads was increasing by 40. tousand downloads per week. Instantaneous rate of cange at x=9: = C. Between six and nine weeks after te initial release of te single #selfie, te total number of downloads increased on average by tousand downloads per week. average rate of cange between x=6 and x=9: = D. Between six and nine weeks after te initial release of te single #selfie, te total number of downloads increased by %. percent cange between x=6 and x=9: = ( / 8pts ) Page 10/1

11 4. Use te limit definition of te derivative to find te derivative of f( x) = 4x 1.5x+ 6. For full credit, continue from te general limit definition (provided below), clearly sowing all necessary algebraic steps (cancellations, expansions, etc.) and including proper use of notation and equal signs. f ( x) = lim 0 f( x+ ) f( x) [4( ) 1.5( ) 6] [ ] x+ x+ + x x+ = lim 0 [4( x + x + ) 1.5( x + ) + 6] [4x 1.5x + 6] = lim 0 4x + 8x x x + 1.5x 6 = lim 0 8x (8x ) = lim = lim 0 0 = lim(8x ) 0 = 8x 1.5 Tus, f ( x) = 8x pts: Find slope of secant using given function: [f(x+) f(x)]/ 1 pt: Square (x+) correctly pts: Distribute 4, -1.5, and te -1 (minus sign) correctly 1 pt: Combine like terms and sow te result. 1 pt: Sow te limit of a completely simplified expression 1 pt: Evaluate limit of simplified expression to find derivative. Deductions: up to 1.5 pts if limit notation is missing; -½ pt if te limit notation is written incorrectly trougout proof -½ pt if equal signs not in correct places and used trougout ( / 9 pts ) 1 point for correctly filling out and bubbling te scantron wit a # pencil, a correct XID, a correct test version AND te front of te test is completed wit your signature on te academic integrity statement. END OF TEST Page 11/1

12 General Directions: Sow work were possible. Answers witout supporting work (were work is appropriate) may receive little credit. Do not round intermediate calculations. Answers in context ALWAYS require units. Assume end of te year data unless stated oterwise. Round your answers to 3 decimal places UNLESS te answer needs to be rounded differently to make sense in te context of te problem OR te directions specify anoter type rounding OR te complete answer as fewer tan 3 decimal places. Wen asked to write a model, include all components of a model: an equation, a description of te input including units, a description of te output including units, and te input interval wen known. Wen asked to write a sentence of practical interpretation, answer te questions: wen?, wat?, and ow muc? using ordinary, conversational language. DO NOT use mat words, terms, or unnecessary prases. Always use a ruler wen estimating values off of a grap. HINTS FOR TROUBLESHOOTING YOUR CALCULATOR: If you lose your L1, L, etc., you may reinsert tem using STAT 5 (set-up editor) enter. Te SCATTER PLOT will not sow unless Plot 1 as been turned on and tere is data in L1 and L. ZOOM 0 may not work for graping if Plot 1 is turned on. DIM MISMATCH error usually means tat te lists in L1 and L are not of equal lengt. DATA TYPE error usually means tat you already ave someting in Y1 and you need to clear it before you can paste a new equation. INVALID DIM error usually means tat your plot(s) are on, but tat you ave no data in te lists. Refer to te second int above. If your batteries die, raise your and and old up your calculator. If your instructor as an extra calculator available, e/se will loan it to you for a few minutes. SYNTAX ERROR: Try GO TO. Tis will appen if you use a subtraction minus sign wen you sould use a negative sign. MATH SOLVER only works if tere is a variable x in Y1. If you need to CLEAR MEMORY, use nd +, 7:Reset, 1:All Ram, :Reset Page 1/1