MATH 1020 TEST 2 VERSION A FALL 2014 ANSWER KEY. Printed Name: Section #: Instructor:

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1 ANSWER KEY Printed Name: Section #: Instructor: Please do not ask questions during tis eam. 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. See page two for formulas, general directions, and calculator troublesooting tips. Any communication wit any person (oter tan te instructor or te designated proctor) during tis eam 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 and PDAs must be turned off 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#1 FR # FR #3 FR #4 FR #5 scantron Free Response Total Multiple Coice Total Total Possible points Points Earned Useful Formulas: ( ) f + f ( ) f ( ) = lim ; 0 f ( ) f ( a) f ( a) = lim a a Page 1/1

2 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 contet ALWAYS require units. Round your answers to 3 decimal places UNLESS te answer needs to be rounded differently to make sense in te contet of te problem OR te directions specify anoter type rounding OR te complete answer as less tan 3 decimal places. Wen you are 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 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. IF you set te entire and y window range, use te GRAPH button to see te grap. 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 etra 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. Page /1

3 MULTIPLE CHOICE: 64 points (3 points eac unless oterwise noted) Version A: A C D B D A B D B C C B A D D B A B C C A B C D A 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. 1. If f ( ) = 5e, ten f ( ) =. a. 5 e b. 5ln ( 1) c. 5e d. 5. If f ( ) 6 =, ten f ( ) =. a. 6 1 b. 3 1 c. 3 3 d If f ( ) 3 3 ln =, ten f ( ) =. [ pts] a. 3 1 ln b. 9 1 c. 1 d If f ( ) = 100(1.05 ), ten f ( ) =. [ pts] a. (ln105)(1.05 ) 1 c. 100 (1.05 ) b. 100(ln1.05)(1.05 ) d. 100 (1.05 ) 5. If f ( ) 4 =, ten f ( ) =. a. 4ln b. 4 c. 1 4 d. 4 Page 3/1

4 Use te following information to answer te net four questions. Te grap below sows te global mean temperature in degrees Celsius (C ) between 000 and Global mean temperature was canging te most rapidly in 005. How quickly was te temperature canging in 005? a b c d Wat are te output units for te answer to te previous question? [ pts] a. years per degree C b. degrees C per year c. degrees C d. years 8. Wic ONE of te following is FALSE? [ pts] a. Te slope of te tangent line is positive at point A. b. Te derivative at point B is greater tan te derivative at point C. c. Te tangent line lies below te curve at point D. d. Te instantaneous rate of cange is greatest at B. 9. Wat does te slope of a line tat passes troug te points A and C represent? [ pts] a. Te cange in global mean temperature between 001 and 005. b. Te average rate of cange in global mean temperature between 001 and 005. c. Te rate of cange in global mean temperature between 001 and 005. d. Te percentage cange in global mean temperature between 001 and 005. Page 4/1

5 10. Fill in te blanks to te following sentence by referring to te graps below. On te four graps below, tere are correctly drawn tangent lines and correctly drawn secant lines. Grap A Grap B Grap C Grap D a. two; two b. one; tree c. tree; one d. four; zero 11. Wic ONE of te following is te derivative grap of te function sown to te rigt? a. Grap A b. Grap B c. Grap C d. Grap D Grap A Grap B Grap C Grap D Page 5/1

6 1. b( t ) micrograms per milliliter ( µ g / ml ) gives te concentration level of a certain drug in te blood stream, were t is te number of ours since te drug is dosed. Wic ONE of te following is an INCORRECT statement about b ( t)? a. b ( t) describes te instantaneous rate of cange in te concentration level of te drug in te blood t ours after te drug is dosed. b. b ( t) describes te concentration level of te drug in te blood t ours after te drug is dosed. c. b ( t) describes te slope of te tangent line to a grap sowing te concentration level of te drug in te blood t ours after te drug is dosed. d. b ( t) describes te derivative of te concentration level of te drug in te blood t ours after te drug is dosed. 13. p( t ) tousand people gives te population of a certain town, in te year t. In 014, te population of te town was 56.6 tousand people and te population was decreasing by 0.5 tousand people per year. Wic ONE of te following follows from te given information? a. p (014) = 56.6 and dp dt t= 014 = 0.5 b. p (014) = 0.5 and dp dt t= 014 = 56.6 b. p (014) = 0.5 and dt = 56.6 d. p (014) = 56.6 and dp = p 14 dt = 0.5 dp = p Te yearly profit for a small cloting company is given by P() tousand dollars, were is te number of years after 000. P(6)= 0.143, P'(6)= 4.45, and P(7)= Find te percentage rate of cange in te company s profit in 006. a % per year b % per year c % per year d..10 % per year Page 6/1

7 15. In using te limit definition of te derivative for a function f ( ), one finds f ( ) = lim Wic ONE of te following epressions is equal to lim? 0 a. lim( ) b c d lim 16. A function F( v) sows ow driving speed affects fuel economy. F( v) is measured in miles per gallon and speed v is measured in miles per our. Sketc a grap of te function F( v) wit te following properties: F (50) = 30, F (50) = 0, F (30) > 0, F (70) < 0 a. b. c. d. Page 7/1

8 Use te following information to answer te net tree questions. [ pts eac] Te grap below sows US cattle prices for 450-pound calves from October 1994 troug April On wat interval(s) is te instantaneous rate of cange in cattle prices positive? a. 0< m< 3 b. 3< m< 6 c. 0< m< 3and3< m< 6 P(m) dollars per pound d. nowere 0.83 m monts since October Fill in te blanks to complete te sentence: in January 1995, wen m= 3, te grap of P( m) sows tat te function is and tat te instantaneous rate of cange. a. continuous; eists b. continuous; does not eist c. not continuous; eists d. not continuous; does not eist 19. Identify te correct derivative grap of P( m ). Grap A Grap B Grap C Grap D a. Grap A b. Grap B c. Grap C d. Grap D Page 8/1

9 Use te following SLOPE graps to answer te net two questions. GRAPH A GRAPH B GRAPH C GRAPH D 0. Wic one of te above graps is te correct slope grap for te grap of te function to te rigt? f () a. Grap A b. Grap B c. Grap C d. Grap D 1. Wic one of te above graps is te correct slope grap for te grap of te function to te rigt? f () a. Grap A b. Grap B c. Grap C d. Grap D Use te following information to answer te net two questions: 0.84t According to te Apple Corporation s annual reports, s( t) = e million dollars gives Apple s annual sales, t years after 000, 1 t 10. ceckpoint: s() Find te average rate of cange in Apple s annual sales between 005 and 008. a. 18, b. 6, c d Wat are te units for te average rate of cange calculated in te previous question? [ pts] a. million dollars b. percent c. million dollars per year d. percent per year Page 9/1

10 Use te following information to te complete te sentences in te net two questions. [ pts eac] After earing rumors tat te ipone 6 may bend wen carried in one s front pocket, a Mat 100 instructor eperimented by carrying te pone in er front pocket. Se recorded te angle of bend, in degrees, every two ours. Te table below gives te results. Hours since pone placed in pocket Angle of bend, in degrees Between te 4 t and 8 t ours, te ipone 6 s angle of bend increased by degrees. a b. 1.3 c. 0.8 d Between te 4 t and 8 t ours, te ipone 6 s angle of bend increased by percent. a b c..750 d FREE RESPONSE: 36 points Sow work were possible. Read te directions on rounding, inclusion of units, and writing models and sentences at te front of te test. t 1. P( t ) = 0.16(1.048 ) people per square mile gives te population density in Nevada, t years after 1900, 0 t 97. ceckpoint: P(3) a. How quickly was Nevada s population density canging in 1965? Include units wit your answer, correct to 3 decimal places. a) 1 pt. numeric portion (Note: use nderiv) P (65) = pt units people per square mile per year b) 1 pt equation 1 pt units 1 pt rate of cange in 1 pt Nevada s population density b. Find te derivative of P( t) and write a completely defined RATE OF CHANGE model: dp dt = 0.16(ln1.048)(1.048 t ) people per square mile per year (equation) (units) gives te rate of cange in Nevada s population density, (description) t years after 1900, 0 t 97. ( / 6pts ) Page 10/1

11 . Tere were 3,53 students enrolled at Clemson's main campus in In 1987, Clemson ad 1,870 students enrolled at te main campus. Find te average rate of cange of students enrolled at te main campus from 1947 to 1987, correct to 3 decimal places. Write your answer in a sentence of interpretation = ½ pt. wen pt output description 1 pt increased Between 1947 and 1987, te number of students enrolled at Clemson s main ½ pt on average by campus increased on average by students per year. 1 pt number 1 pt units ( / 5pts ) t 3 3e+ 11t + 11t 3. Te function N( t) = gives te total number of bacteria in a petri dis t weeks after te t + 1 start of an eperiment, 0 t 1. Ceckpoint: N() a. Fill in te following table, correct to 3 decimal places, to numerically estimate te instantaneous rate of cange of N( t ) at t= 6. t 6 N ( t) N (6) t 6 + t 6 N ( t) N (6) t b. Eac entry in te table for N ( t) N (6) t 6 represents (circle one): te slope of a secant line on te grap of N( t ) OR te slope of te tangent line to N( t) at t= 6 c. According to te table N (6) = (correct to 3 decimal places) a) 4 pts b) ½ pt c) ½ pt d) 1 pt wen 1 pt output description 1 pt increasing by 1 pt number wit units d. Write a sentence of interpretation for te answer to part c). Si weeks after te start of an eperiment, te bacteria in a petri dis were increasing by bacteria per week. ONE MORE PAGE.. ( / 9pts ) Page 11/1

12 4. Find te derivative for eac of te given functions. Simplify eponents and coefficients, and use eact numbers. For full credit, sow work clearly and include proper use of derivative notation and equal signs ( / 6 pts ) a. f ( ) = b. g( ) = 5ln π e 3 f ( ) = pts: ½ pt notation, 1 pt per term 5 g ( ) = πe.5 pts: ½ pt notation, 1 pt per term 5. Use te limit definition of te derivative to find te derivative of f ( ) = (Ceck your answer using simple rate of cange formulas.) For full credit, continue from te general limit definition (provided below), clearly sowing all necessary algebraic steps (cancellations, epansions, etc.) and including proper use of notation and equal signs. f ( + ) f ( ) f ( ) = lim 0 [1.5( + ) ( + ) + 9] [ ] = lim 0 [1.5( + + ) ( + ) + 9] [ ] = lim = lim ( ) = lim = lim 0 0 = lim( ) 0 = 3 Tus, f ( ) = 3 3 pts: Find slope of secant using given function: [f(+) f()]/ 1 pt: Square (+) correctly pts: Distribute 1.5, -, and -1 correctly 1 pt: Combine like terms and sow te result; factor out and cancel, sowing te limit of a completely simplified epression. 1 pt: Evaluate limit of simplified epression to find derivative. ½ pt correctly written limit notation trougout proof ½ pt: equal signs in correct places and used trougout proof ( / 9 pts ) 6. If your scantron is correctly bubbled wit a # pencil, wit your correct XID, your correct test version, AND te front of your test is completed wit your signature on te academic integrity statement, you earn 1 point. END OF TEST Page 1/1