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1 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. 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 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, 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#1 FR #2 FR #3 FR #4 FR #5 FR #6 scan tron Free Respons e Total Multiple Coice Total Total Possible Points Points Earned Useful Formulas: ( ) f + f ( ) f ( ) = lim ; 0 f ( ) f ( a) f ( a) = lim a a rt r F( t) = P(1 + rt) F( t) = Pe F( t) = P 1+ n r r APY = ( e 1)100% or APY = % n n ( nt) Page 1/12

2 MULTIPLE CHOICE: 61 points (3 points eac, unless oterwise noted) Use a #2 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. A C D B A D C A B B D C D A B D C C A B A C 1. Suppose $1000 is deposited in a bank, earning interest at an annual percentage rate (APR) of 2.5% compounded quarterly. If tere are no oter deposits or witdrawals, find te future value of tis deposit after 22 monts. a. $ b. $ c. $ d. $ A bank offers an investment of $1000 an annual percentage rate (APR) of 1.8% compounded quarterly. If tere are no oter deposits or witdrawals, ow long will it take te investment to double? a. 38 years 5 monts b. 38 years 6 monts c. 38 years 9 monts d years 3. Wic bank rate offers te igest annual percentage yield for a deposit in an account? Bank A account, wit an annual percentage yield (APY) of 4.444% after compounding semi-annually. Bank B account, offering an annual percentage rate (APR) of 4.36% compounded quarterly. Bank C account, wit an annual percentage yield (APY) of 4.438% after compounding montly. Bank D account, offering an annual percentage rate (APR) of 4.35% compounded continuously. a. Bank A b. Bank B c. Bank C d. Bank D 4. Find te derivative s ( ) = for s( ) = 2(1.3 ). a. 2ln(1.3 )(1.3 ) b. 2ln(1.3)(1.3 ) c. ln(2.6)(2.6 ) d. 1 2 (1.3 ) 5. Te slope of te tangent line to a point on te grap of function C( ) = 3ln( ) is. a. 3 b. 3e c. 1 3 d. 3 Page 2/12

3 6. Find f ( ) = for f = e+ e. 5 ( ) 2 3 a. 4 + b. 10e + 3ln( ) 5 2e 3e 4 1 c. 10e + 3e d. 3e dr 4 7. If r( ) = 8, ten. d = a b c d Wic one of te following could be te grap of f, if f is a function wit te following caracteristics? f (2) > 0, and f (5) does not eist, and f (6) < 0 a. b. c. d. Page 3/12

4 Use te grap of f ( ) given below to answer te net four questions. 9. [ 2 pts] Te function f ( ) is at = 4. a. continuous and its derivative eists b. continuous and its derivative does not eist c. not continuous and its derivative eists d. not continuous and its derivative does not eist 10. [ 2 pts] Identify ALL values of for wic te derivative f ( ) = 0. a. = 1.5, = 1 b. = 3, = 0, = 2 c. = 4.1, = 0, = 3.1, = 5.1 d. = 3, = 0, = 2, = [ 2 pts] Find te intervals on wic te slope grap of f ( ) lies below te -ais. a. ( 4.4, 4.1), (3.1, 5.1) b. ( 4.4, 1.5), (1, 4) c. ( 3, 1.5), (2, 3.1) only d. ( 3, 0), (2, 4) 12. [ 2 pts] Consider te above grap restricted to te interval ( 4.4, 4). Find te combined number of relative maima and relative minima tat will occur on te slope grap of f ( ). a. zero b. one c. two d. tree Page 4/12

5 Use te following table to answer te net two questions. Te table below sows te price of beef in te United States in January of various years. Year Price of beef, in dollars/pound 13. Between January of 2008 and January of 2015, te price of beef increased on average by dollars/pound per year. a b c d Between January of 2008 and January of 2015, te price of beef increased by %. a b c d Wic one of te following is a slope grap of te function grap sown below? a. b. c. d. Page 5/12

6 16. Wic one of te following is a slope grap of te function grap sown below? a. b. c. d. 17. Given f ( ) =, find f ( ) =. 3 a b. 3 3ln( ) c d Page 6/12

7 Use te following information to answer te net two questions. C( ) billion subscribers gives total number of mobile pone subscribers in te developing world, years since 2000, Draw a line tangent to te grap at te given point (6.5, 1.75) and estimate its slope. (Insert te answer into te net question.) a b. 2.5 c. 0.4 d Write a sentence of interpretation for te slope of te tangent line. a. In mid-2007, te number of mobile pone subscribers in te developing world was increasing by (answer to previous question) billion subscribers per year. b. In mid-2007, te number of mobile pone subscribers in te developing world was increasing by (answer to previous question) billion subscribers. c. Between 2000 and 2010, te number of mobile pone subscribers in te developing world increased by (answer to previous question) billion subscribers per year. d. In mid-2007, te number of mobile pone subscribers in te developing world was increasing by (answer to previous question) % per year. Page 7/12

8 Use te following grap to answer te net tree questions. 20. [2 pts] Consider te point C on te above grap. Te tangent line to te grap at point C is drawn te function curve. a. below b. above c. neiter, it coincides d. bot, it cuts troug 21. Consider te tree points A, B, and C on te grap above. Order te tree points from least steepness to greatest steepness. a. B, C, A b. C, B, A c. A, C, B d. B, A, C 22. Wic one of te following sows a correct tangent line drawn at te inflection point B? a. b. c. d. Page 8/12

9 FREE RESPONSE: 39 points Sow work were possible. Read te directions at te back of te test on rounding, inclusion of units, and writing sentences and models. 1. Te population of Boston, Massacusetts, can be represented by 3 2 P( ) = tousand people, years since 1900, Ceckpoint: P (2) = Give a completely defined rate-of-cange model for P( ) by filling in te blanks: Part a) 5 pts: 2 pts derivative 2 P ( ) = tousand people per year 1 pt units (equation) (units) 1 pt rate of cange 1 pt output gives te rate of cange in te population of Boston, Massacusetts, dedesdescription were is te number of years since 1900, a. How quickly is population canging in 1930? Round to tree decimal places and interpret in a complete sentence. Part B) 5 pts 1 pt wen, 1 pt wat, 1 pt was decreasing by, 1 pt ow muc, 1 pt units In 1930, Boston s population was decreasing by tousand people per year. ( /10 pts) 2. Te number of Bald Eagle breeding pairs in te lower 48 states was 2680 in 1989 and was 4015 in Find te average rate of cange in te number of Bald Eagle breeding pairs from 1989 to 1993 and write te answer in a sentence of interpretation. 1 pt wen, 1 pt wat, pt increased = pts on average by, 1.5 pts ow muc, 1 pt units Between 1989 and 1993, te number of Bald Eagle breeding pairs increased on average by pairs per year. ( / 6 pts ) 3. R( ) billion dollars gives te advertising revenue for a newspaper, years since 1980, In 1990, advertising revenue was 3, billion dollars and was increasing by billion dollars per year. Find percentage rate of cange in te advertising revenue in Sow work, round te answer to tree decimal places, and include units. 1 pt number R (10) = 100 = % per year 1 pt units R(10) ( / 2 pts) Page 9/12

10 4. In te early stages of te deadly SARS (Severe Acute Respiratory Syndrome) epidemic of 2003, te number of reported cases was approimately S( t ) = 167(1.18 t ) cases t days after Marc 17, 2003 (te first day in wic statistics were reported by te World Healt Organization), 0 t 20. a. Use te limit of te slopes of secant lines to numerically estimate S (7). Round entries to eactly 2 decimal places for full credit. t 7 S( t) S(7) t 7 Ceckpoint: S (3) = t 7 S( t) S(7) t Part a) 4 pts entries in table, correct to two decimal places b. S( t) S(7) lim = t 7 t 7 + t 7 S( t) S(7) lim = _ t 7 c. S (7) = cases per day (include units) Part b) 1 pt for te limits, correct to two decimal places. Part c) 0.5 pt for derivative, correct to two decimal places. 1 pt for units d. Circle te correct use of differential notation for S (7). dt ds dt ds ds s = 7 dt s = 7 ds t = 7 dt t = 7 Part d) 0.5 pts Part e) 1.5 pts e. Te number in te above table represents te slope of a secant line on te grap of S( t ) between points t= 6.9 and t= 7 _ ; wereas te answer to part c) represents te slope of a tangent line at t= 7 _. ( /8.5pts) 3 5. Find te derivative of te function f ( ) = 6 3. For full credit, clearly sow work and use proper matematical notation f ( ) = 6 3 = f ( ) = pts notation 1 pt per term ( / 2.5 pts ) Page 10/12

11 2 6. Use te limit definition of te derivative to find te derivative of f ( ) = 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 ( ) = lim 0 f ( + ) f ( ) 2 2 [5( + ) 2.4( + ) + 7] [ ] = lim 0 = lim 0 = lim = lim 0 ( ) = lim 0 = lim( ) 0 = Tus, f ( ) = [5( ) 2.4( + ) + 7] [ ] pts: Find slope of secant using given function: [f(+) f()]/ 1 pt: Square (+) correctly 2 pts: Distribute 5, -2.4, and te -1 (minus sign) correctly 1 pt: Combine like terms and sow te result. 1 pt: Sow te limit of a completely simplified epression 1 pt: Evaluate limit of simplified epression to find derivative. -½ pt if equal signs not in correct places and used trougout proof -1 pt if limit notation is missing ( / 9 pts) 1 point for correctly filling out and bubbling te scantron wit a #2 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 11/12

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 contet 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 contet 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, L2, 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 L2. ZOOM 0 may not work for graping if Plot 1 is turned on. DIM MISMATCH error usually means tat te lists in L1 and L2 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. If you need to CLEAR MEMORY, use 2 nd +, 7:Reset, 1:All Ram, 2:Reset Page 12/12

13 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. 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 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, 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#1 FR #2 FR #3 FR #4 FR #5 FR #6 scan tron Free Respons e Total Multiple Coice Total Total Possible Points Points Earned Useful Formulas: ( ) f + f ( ) f ( ) = lim ; 0 f ( ) f ( a) f ( a) = lim a a rt r F( t) = P(1 + rt) F( t) = Pe F( t) = P 1+ n r r APY = ( e 1)100% or APY = % n n ( nt) Page 1/12

14 MULTIPLE CHOICE: 61 points (3 points eac, unless oterwise noted) Use a #2 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. A C D B A D C A B B D C D A B D C C A B A C 1. Suppose $1000 is deposited in a bank, earning interest at an annual percentage rate (APR) of 2.5% compounded quarterly. If tere are no oter deposits or witdrawals, find te future value of tis deposit after 22 monts. a. $ b. $ c. $ d. $ A bank offers an investment of $1000 an annual percentage rate (APR) of 1.8% compounded quarterly. If tere are no oter deposits or witdrawals, ow long will it take te investment to double? a. 38 years 5 monts b. 38 years 6 monts c. 38 years 9 monts d years 3. Wic bank rate offers te igest annual percentage yield for a deposit in an account? Bank A account, wit an annual percentage yield (APY) of 4.444% after compounding semi-annually. Bank B account, offering an annual percentage rate (APR) of 4.36% compounded quarterly. Bank C account, wit an annual percentage yield (APY) of 4.438% after compounding montly. Bank D account, offering an annual percentage rate (APR) of 4.35% compounded continuously. a. Bank A b. Bank B c. Bank C d. Bank D 4. Find te derivative s ( ) = for s( ) = 2(1.3 ). a. 2ln(1.3 )(1.3 ) b. 2ln(1.3)(1.3 ) c. ln(2.6)(2.6 ) d. 1 2 (1.3 ) 5. Te slope of te tangent line to a point on te grap of function C( ) = 3ln( ) is. a. 3 b. 3e c. 1 3 d. 3 Page 2/12

15 6. Find f ( ) = for f = e+ e. 5 ( ) 2 3 a. 4 + b. 10e + 3ln( ) 5 2e 3e 4 1 c. 10e + 3e d. 3e dr 4 7. If r( ) = 8, ten. d = a b c d Wic one of te following could be te grap of f, if f is a function wit te following caracteristics? f (2) > 0, and f (5) does not eist, and f (6) < 0 a. b. c. d. Page 3/12

16 Use te grap of f ( ) given below to answer te net four questions. 9. [ 2 pts] Te function f ( ) is at = 4. a. continuous and its derivative eists b. continuous and its derivative does not eist c. not continuous and its derivative eists d. not continuous and its derivative does not eist 10. [ 2 pts] Identify ALL values of for wic te derivative f ( ) = 0. a. = 1.5, = 1 b. = 3, = 0, = 2 c. = 4.1, = 0, = 3.1, = 5.1 d. = 3, = 0, = 2, = [ 2 pts] Find te intervals on wic te slope grap of f ( ) lies below te -ais. a. ( 4.4, 4.1), (3.1, 5.1) b. ( 4.4, 1.5), (1, 4) c. ( 3, 1.5), (2, 3.1) only d. ( 3, 0), (2, 4) 12. [ 2 pts] Consider te above grap restricted to te interval ( 4.4, 4). Find te combined number of relative maima and relative minima tat will occur on te slope grap of f ( ). a. zero b. one c. two d. tree Page 4/12

17 Use te following table to answer te net two questions. Te table below sows te price of beef in te United States in January of various years. Year Price of beef, in dollars/pound 13. Between January of 2008 and January of 2015, te price of beef increased on average by dollars/pound per year. a b c d Between January of 2008 and January of 2015, te price of beef increased by %. a b c d Wic one of te following is a slope grap of te function grap sown below? a. b. c. d. Page 5/12

18 16. Wic one of te following is a slope grap of te function grap sown below? a. b. c. d. 17. Given f ( ) =, find f ( ) =. 3 a b. 3 3ln( ) c d Page 6/12

19 Use te following information to answer te net two questions. C( ) billion subscribers gives total number of mobile pone subscribers in te developing world, years since 2000, Draw a line tangent to te grap at te given point (6.5, 1.75) and estimate its slope. (Insert te answer into te net question.) a b. 2.5 c. 0.4 d Write a sentence of interpretation for te slope of te tangent line. a. In mid-2007, te number of mobile pone subscribers in te developing world was increasing by (answer to previous question) billion subscribers per year. b. In mid-2007, te number of mobile pone subscribers in te developing world was increasing by (answer to previous question) billion subscribers. c. Between 2000 and 2010, te number of mobile pone subscribers in te developing world increased by (answer to previous question) billion subscribers per year. d. In mid-2007, te number of mobile pone subscribers in te developing world was increasing by (answer to previous question) % per year. Page 7/12

20 Use te following grap to answer te net tree questions. 20. [2 pts] Consider te point C on te above grap. Te tangent line to te grap at point C is drawn te function curve. a. below b. above c. neiter, it coincides d. bot, it cuts troug 21. Consider te tree points A, B, and C on te grap above. Order te tree points from least steepness to greatest steepness. a. B, C, A b. C, B, A c. A, C, B d. B, A, C 22. Wic one of te following sows a correct tangent line drawn at te inflection point B? a. b. c. d. Page 8/12

21 FREE RESPONSE: 39 points Sow work were possible. Read te directions at te back of te test on rounding, inclusion of units, and writing sentences and models. 1. Te population of Boston, Massacusetts, can be represented by 3 2 P( ) = tousand people, years since 1900, Ceckpoint: P (2) = Give a completely defined rate-of-cange model for P( ) by filling in te blanks: Part a) 5 pts: 2 pts derivative 2 P ( ) = tousand people per year 1 pt units (equation) (units) 1 pt rate of cange 1 pt output gives te rate of cange in te population of Boston, Massacusetts, dedesdescription were is te number of years since 1900, a. How quickly is population canging in 1930? Round to tree decimal places and interpret in a complete sentence. Part B) 5 pts 1 pt wen, 1 pt wat, 1 pt was decreasing by, 1 pt ow muc, 1 pt units In 1930, Boston s population was decreasing by tousand people per year. ( /10 pts) 2. Te number of Bald Eagle breeding pairs in te lower 48 states was 2680 in 1989 and was 4015 in Find te average rate of cange in te number of Bald Eagle breeding pairs from 1989 to 1993 and write te answer in a sentence of interpretation. 1 pt wen, 1 pt wat, pt increased = pts on average by, 1.5 pts ow muc, 1 pt units Between 1989 and 1993, te number of Bald Eagle breeding pairs increased on average by pairs per year. ( / 6 pts ) 3. R( ) billion dollars gives te advertising revenue for a newspaper, years since 1980, In 1990, advertising revenue was 3, billion dollars and was increasing by billion dollars per year. Find percentage rate of cange in te advertising revenue in Sow work, round te answer to tree decimal places, and include units. 1 pt number R (10) = 100 = % per year 1 pt units R(10) ( / 2 pts) Page 9/12

22 4. In te early stages of te deadly SARS (Severe Acute Respiratory Syndrome) epidemic of 2003, te number of reported cases was approimately S( t ) = 167(1.18 t ) cases t days after Marc 17, 2003 (te first day in wic statistics were reported by te World Healt Organization), 0 t 20. a. Use te limit of te slopes of secant lines to numerically estimate S (7). Round entries to eactly 2 decimal places for full credit. t 7 S( t) S(7) t 7 Ceckpoint: S (3) = t 7 S( t) S(7) t Part a) 4 pts entries in table, correct to two decimal places b. S( t) S(7) lim = t 7 t 7 + t 7 S( t) S(7) lim = _ t 7 c. S (7) = cases per day (include units) Part b) 1 pt for te limits, correct to two decimal places. Part c) 0.5 pt for derivative, correct to two decimal places. 1 pt for units d. Circle te correct use of differential notation for S (7). dt ds dt ds ds s = 7 dt s = 7 ds t = 7 dt t = 7 Part d) 0.5 pts Part e) 1.5 pts e. Te number in te above table represents te slope of a secant line on te grap of S( t ) between points t= 6.9 and t= 7 _ ; wereas te answer to part c) represents te slope of a tangent line at t= 7 _. ( /8.5pts) 3 5. Find te derivative of te function f ( ) = 6 3. For full credit, clearly sow work and use proper matematical notation f ( ) = 6 3 = f ( ) = pts notation 1 pt per term ( / 2.5 pts ) Page 10/12

23 2 6. Use te limit definition of te derivative to find te derivative of f ( ) = 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 ( ) = lim 0 f ( + ) f ( ) 2 2 [5( + ) 2.4( + ) + 7] [ ] = lim 0 = lim 0 = lim = lim 0 ( ) = lim 0 = lim( ) 0 = Tus, f ( ) = [5( ) 2.4( + ) + 7] [ ] pts: Find slope of secant using given function: [f(+) f()]/ 1 pt: Square (+) correctly 2 pts: Distribute 5, -2.4, and te -1 (minus sign) correctly 1 pt: Combine like terms and sow te result. 1 pt: Sow te limit of a completely simplified epression 1 pt: Evaluate limit of simplified epression to find derivative. -½ pt if equal signs not in correct places and used trougout proof -1 pt if limit notation is missing ( / 9 pts) 1 point for correctly filling out and bubbling te scantron wit a #2 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 11/12

24 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. 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 contet 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, L2, 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 L2. ZOOM 0 may not work for graping if Plot 1 is turned on. DIM MISMATCH error usually means tat te lists in L1 and L2 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. If you need to CLEAR MEMORY, use 2 nd +, 7:Reset, 1:All Ram, 2:Reset Page 12/12

25 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. 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 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, 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#1 FR #2 FR #3 FR #4 FR #5 FR #6 scan tron Free Respons e Total Multiple Coice Total Total Possible Points Points Earned Useful Formulas: ( ) f + f ( ) f ( ) = lim ; 0 f ( ) f ( a) f ( a) = lim a a rt r F( t) = P(1 + rt) F( t) = Pe F( t) = P 1+ n r r APY = ( e 1)100% or APY = % n n ( nt) Page 1/12

26 MULTIPLE CHOICE: 61 points (3 points eac, unless oterwise noted) Use a #2 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. A C D B A D C A B B D C D A B D C C A B A C 1. Suppose $1000 is deposited in a bank, earning interest at an annual percentage rate (APR) of 2.5% compounded quarterly. If tere are no oter deposits or witdrawals, find te future value of tis deposit after 22 monts. a. $ b. $ c. $ d. $ A bank offers an investment of $1000 an annual percentage rate (APR) of 1.8% compounded quarterly. If tere are no oter deposits or witdrawals, ow long will it take te investment to double? a. 38 years 5 monts b. 38 years 6 monts c. 38 years 9 monts d years 3. Wic bank rate offers te igest annual percentage yield for a deposit in an account? Bank A account, wit an annual percentage yield (APY) of 4.444% after compounding semi-annually. Bank B account, offering an annual percentage rate (APR) of 4.36% compounded quarterly. Bank C account, wit an annual percentage yield (APY) of 4.438% after compounding montly. Bank D account, offering an annual percentage rate (APR) of 4.35% compounded continuously. a. Bank A b. Bank B c. Bank C d. Bank D 4. Find te derivative s ( ) = for s( ) = 2(1.3 ). a. 2ln(1.3 )(1.3 ) b. 2ln(1.3)(1.3 ) c. ln(2.6)(2.6 ) d. 1 2 (1.3 ) 5. Te slope of te tangent line to a point on te grap of function C( ) = 3ln( ) is. a. 3 b. 3e c. 1 3 d. 3 Page 2/12

27 6. Find f ( ) = for f = e+ e. 5 ( ) 2 3 a. 4 + b. 10e + 3ln( ) 5 2e 3e 4 1 c. 10e + 3e d. 3e dr 4 7. If r( ) = 8, ten. d = a b c d Wic one of te following could be te grap of f, if f is a function wit te following caracteristics? f (2) > 0, and f (5) does not eist, and f (6) < 0 a. b. c. d. Page 3/12

28 Use te grap of f ( ) given below to answer te net four questions. 9. [ 2 pts] Te function f ( ) is at = 4. a. continuous and its derivative eists b. continuous and its derivative does not eist c. not continuous and its derivative eists d. not continuous and its derivative does not eist 10. [ 2 pts] Identify ALL values of for wic te derivative f ( ) = 0. a. = 1.5, = 1 b. = 3, = 0, = 2 c. = 4.1, = 0, = 3.1, = 5.1 d. = 3, = 0, = 2, = [ 2 pts] Find te intervals on wic te slope grap of f ( ) lies below te -ais. a. ( 4.4, 4.1), (3.1, 5.1) b. ( 4.4, 1.5), (1, 4) c. ( 3, 1.5), (2, 3.1) only d. ( 3, 0), (2, 4) 12. [ 2 pts] Consider te above grap restricted to te interval ( 4.4, 4). Find te combined number of relative maima and relative minima tat will occur on te slope grap of f ( ). a. zero b. one c. two d. tree Page 4/12

29 Use te following table to answer te net two questions. Te table below sows te price of beef in te United States in January of various years. Year Price of beef, in dollars/pound 13. Between January of 2008 and January of 2015, te price of beef increased on average by dollars/pound per year. a b c d Between January of 2008 and January of 2015, te price of beef increased by %. a b c d Wic one of te following is a slope grap of te function grap sown below? a. b. c. d. Page 5/12

30 16. Wic one of te following is a slope grap of te function grap sown below? a. b. c. d. 17. Given f ( ) =, find f ( ) =. 3 a b. 3 3ln( ) c d Page 6/12

31 Use te following information to answer te net two questions. C( ) billion subscribers gives total number of mobile pone subscribers in te developing world, years since 2000, Draw a line tangent to te grap at te given point (6.5, 1.75) and estimate its slope. (Insert te answer into te net question.) a b. 2.5 c. 0.4 d Write a sentence of interpretation for te slope of te tangent line. a. In mid-2007, te number of mobile pone subscribers in te developing world was increasing by (answer to previous question) billion subscribers per year. b. In mid-2007, te number of mobile pone subscribers in te developing world was increasing by (answer to previous question) billion subscribers. c. Between 2000 and 2010, te number of mobile pone subscribers in te developing world increased by (answer to previous question) billion subscribers per year. d. In mid-2007, te number of mobile pone subscribers in te developing world was increasing by (answer to previous question) % per year. Page 7/12

32 Use te following grap to answer te net tree questions. 20. [2 pts] Consider te point C on te above grap. Te tangent line to te grap at point C is drawn te function curve. a. below b. above c. neiter, it coincides d. bot, it cuts troug 21. Consider te tree points A, B, and C on te grap above. Order te tree points from least steepness to greatest steepness. a. B, C, A b. C, B, A c. A, C, B d. B, A, C 22. Wic one of te following sows a correct tangent line drawn at te inflection point B? a. b. c. d. Page 8/12

33 FREE RESPONSE: 39 points Sow work were possible. Read te directions at te back of te test on rounding, inclusion of units, and writing sentences and models. 1. Te population of Boston, Massacusetts, can be represented by 3 2 P( ) = tousand people, years since 1900, Ceckpoint: P (2) = Give a completely defined rate-of-cange model for P( ) by filling in te blanks: Part a) 5 pts: 2 pts derivative 2 P ( ) = tousand people per year 1 pt units (equation) (units) 1 pt rate of cange 1 pt output gives te rate of cange in te population of Boston, Massacusetts, dedesdescription were is te number of years since 1900, a. How quickly is population canging in 1930? Round to tree decimal places and interpret in a complete sentence. Part B) 5 pts 1 pt wen, 1 pt wat, 1 pt was decreasing by, 1 pt ow muc, 1 pt units In 1930, Boston s population was decreasing by tousand people per year. ( /10 pts) 2. Te number of Bald Eagle breeding pairs in te lower 48 states was 2680 in 1989 and was 4015 in Find te average rate of cange in te number of Bald Eagle breeding pairs from 1989 to 1993 and write te answer in a sentence of interpretation. 1 pt wen, 1 pt wat, pt increased = pts on average by, 1.5 pts ow muc, 1 pt units Between 1989 and 1993, te number of Bald Eagle breeding pairs increased on average by pairs per year. ( / 6 pts ) 3. R( ) billion dollars gives te advertising revenue for a newspaper, years since 1980, In 1990, advertising revenue was 3, billion dollars and was increasing by billion dollars per year. Find percentage rate of cange in te advertising revenue in Sow work, round te answer to tree decimal places, and include units. 1 pt number R (10) = 100 = % per year 1 pt units R(10) ( / 2 pts) Page 9/12

34 4. In te early stages of te deadly SARS (Severe Acute Respiratory Syndrome) epidemic of 2003, te number of reported cases was approimately S( t ) = 167(1.18 t ) cases t days after Marc 17, 2003 (te first day in wic statistics were reported by te World Healt Organization), 0 t 20. a. Use te limit of te slopes of secant lines to numerically estimate S (7). Round entries to eactly 2 decimal places for full credit. t 7 S( t) S(7) t 7 Ceckpoint: S (3) = t 7 S( t) S(7) t Part a) 4 pts entries in table, correct to two decimal places b. S( t) S(7) lim = t 7 t 7 + t 7 S( t) S(7) lim = _ t 7 c. S (7) = cases per day (include units) Part b) 1 pt for te limits, correct to two decimal places. Part c) 0.5 pt for derivative, correct to two decimal places. 1 pt for units d. Circle te correct use of differential notation for S (7). dt ds dt ds ds s = 7 dt s = 7 ds t = 7 dt t = 7 Part d) 0.5 pts Part e) 1.5 pts e. Te number in te above table represents te slope of a secant line on te grap of S( t ) between points t= 6.9 and t= 7 _ ; wereas te answer to part c) represents te slope of a tangent line at t= 7 _. ( /8.5pts) 3 5. Find te derivative of te function f ( ) = 6 3. For full credit, clearly sow work and use proper matematical notation f ( ) = 6 3 = f ( ) = pts notation 1 pt per term ( / 2.5 pts ) Page 10/12

35 2 6. Use te limit definition of te derivative to find te derivative of f ( ) = 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 ( ) = lim 0 f ( + ) f ( ) 2 2 [5( + ) 2.4( + ) + 7] [ ] = lim 0 = lim 0 = lim = lim 0 ( ) = lim 0 = lim( ) 0 = Tus, f ( ) = [5( ) 2.4( + ) + 7] [ ] pts: Find slope of secant using given function: [f(+) f()]/ 1 pt: Square (+) correctly 2 pts: Distribute 5, -2.4, and te -1 (minus sign) correctly 1 pt: Combine like terms and sow te result. 1 pt: Sow te limit of a completely simplified epression 1 pt: Evaluate limit of simplified epression to find derivative. -½ pt if equal signs not in correct places and used trougout proof -1 pt if limit notation is missing ( / 9 pts) 1 point for correctly filling out and bubbling te scantron wit a #2 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 11/12

36 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. 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 contet 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, L2, 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 L2. ZOOM 0 may not work for graping if Plot 1 is turned on. DIM MISMATCH error usually means tat te lists in L1 and L2 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. If you need to CLEAR MEMORY, use 2 nd +, 7:Reset, 1:All Ram, 2:Reset Page 12/12