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1 Calculus for the Life Sciences nd Edition Greenwell Test Bank Full Download: MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the graph to the function. ) ) A) f() = B) f() = + C) f() = - D) f() = A) f() =-0 B) f() = C) f() = 0 D) f() = 0 Full download all chapters instantl please go to Solutions Manual, Test Bank site: testbanklive.com

2 ) A) f() = - B) f() = - - C) f() = - D) f() = ) A) f() = - B) f() = - - C) f() = D) f() = - -

3 5) A) f() = - - B) f() = - C) f() = D) f() = - ) A) f() = -(7) B) f() = C) f() = - 7 D) f() = (7)

4 7) A) f() = 5 B) f() = 5 - C) f() = 5 + D) f() = 5 - ) A) f() = 5 - B) f() = 5 + C) f() = 5 D) f() = 5 -

5 9) A) = - B) = + C) = - - D) = - 0) A) = B) = C) = D) =

6 Solve the equation. ) = A) B) C) D) ) - = A) B) C) - D) ) ( - ) = 79 A) B) C) D) - ) ( + ) = 7 A) B) C) 9 D) - 5) (7 - ) = A) B) - C) D)

7 ) 5 = 5 A) B) C) 5 D) - 7) (7 + ) = A) B) C) - D) ) e - = (e 7 ) - A) 5 B) 5 C) - 5 D) 0 9) - = A), - B), - C) D), - Graph the function. 7

8 0) = e A) B)

9 C) D) ) = -e

10 A) B) C)

11 D) ) = 5e A)

12 B) C) D)

13 ) = e A) B)

14 C) D) ) = -e -/

15 A) B) C)

16 D) Solve the problem. 5) Find the amount of interest earned on the following deposit: $000 at % compounded annuall for ears A) $59.5 B) $9. C) $59.5 D) $50. ) How long will it take for prices in the econom to double at a 5% annual inflation rate? Round to the nearest hundredth when necessar. A).5 r B).5 r C). r D).9 r 7) An economist predicts that the buing power B() of a dollar ears from now will decrease according to the formula B() = 0.. How much will toda's dollar be worth in ears? Round to the nearest cent. A) $0.0 B) $0.79 C) $. D) $. ) Find the interest earned on $,000 invested for 5 ears at.7% interest compounded quarterl. Round to the nearest cent. A) $.7 B) $.9 C) $5,.7 D) $97.77

17 9) Find the interest earned on $9000 invested for ears at.% interest compounded monthl. Round to the nearest cent. A) $5.0 B) $7.9 C) $55.0 D) $5.9 0) Suppose that the number of bacteria in a culture after hours is given b f() = How man bacteria are in the culture after 0 hours? A), bacteria B), bacteria C) 777 bacteria D) bacteria ) Suppose that the number of bacteria in a culture after hours is given b f() = How man bacteria are in the culture after hours? A) 9 bacteria B),000 bacteria C) bacteria D) bacteria ) The population of a particular cit is increasing at a rate proportional to its size. It follows the function P(t) = + ke0.0t where k is a constant and t is the time in ears. If the current population is 7,000, in how man ears is the population epected to be 9,500? A) 7 r B) 0 r C) r D) r ) The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes b D = 900(5), where is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at = 0 and =. A),000; 5,750,000 B) 900; 5,750,000 C) 900;,750,000 D) 900;,000 ) The number of bacteria growing in an incubation culture increases with time according to B = 700(5), where is time in das. Find the number of bacteria when = 0 and =. A) 9,000 bacteria,,75,000 bacteria B) 700 bacteria,,75,000 bacteria C) 700 bacteria, 5,000 bacteria D) 700 bacteria,,75,000 bacteria 7

18 5) The number of books in a small librar increases according to the function B = 500e0.0t, where t is measured in ears. How man books will the librar have after 9 ears? A) 90 books B) 0 books C) 7 books D) 5 books Write the eponential equation in logarithmic form. ) 7 = 9 A) log 9 = 7 B) log9 7 = C) log7 = 9 D) log7 9 = 7) = A) log = B) log = C) log = D) log = ) - = A) log = - B) log - = C) log- = D) log/ = - 9) - = 9 A) log / (-) = 9 B) log /9 (-) = C) log / 9 = - D) log/9 = -

19 Write the logarithmic equation in eponential form. 0) log = - A) = B) - = C) = D) = ) log = A) = B) = C) = D) = ) log = -5 A) 0-5 = B) = -5 C) = 0 D) -50 = ) log = A) = + B) = C) = D) = ) log 00 = A) 0 = 00 B) 0 = 00 C) 0 = 000 D) 0 = 9

20 5) ln = 7 A) 7 = e B) e = 7 C) e 7 = D) 7 e = ) ln e = - A) e - = e B) - e = e C) e - = e D) e e = - 7) ln e = A) ln e = e B) e = e C) e = D) ln = ) ln e / = A) e = e / B) e / = e / C) e / = D) ln = e/ Evaluate the logarithm without using a calculator. 9) log A) B) C) D) 0

21 50) log A) - B) C) 0 D) 5) log7 9 A) -7 B) 7 C) - D) 5) log0 0 A) 0 B) 0 C) - D) 5) log9 79 A) - B) C) - D) 5) log A) 5 B) C) D) 5 55) ln e A) - B) 0 C) e D)

22 5) ln l A) - B) e C) 0 D) 57) log A) - B) C) - D) 5) ln e 5/7 A) 7 5 B) 7 5 e C) 5 7 e D) 5 7 Rewrite the epression as a sum, difference, or product of simpler logarithms. 59) log A) log + log B) log - log C) log + log D) log - log 0) log A) log - log B) log + log C) log - log D) log + log

23 ) log 9 0 A) log 9 + log 0 B) log 0 - log 9 C) log 9 - log 0 D) log 9 - log 0 ) log A) B) C) log + log log - log log - log D) log - log ) log5 p 5k A) log5p - log55k B) log 5log5p log5k C) log5 + log5p - - log5k D) log 5 + log5p + log5k ) log5 5 A) log 5 + 5log5 log5 B) log5 + 5 log 5 log 5 C) log5 + 5 log 5 - log 5 D) log5 + 5log5 - log5

24 Use the properties of logarithms to find the value of the epression. 5) Let logb A = and logb B = -. Find logb AB. A) - B) - C) D) 5 ) Let logb A = and logb B = -0. Find logb A B. A) B) - 5 C) - D) 5 7) Let logb A = and logb B = -. Find logb B. A) - B) C) D) - ) Let logb A = and logb B = -. Find logb AB. A) - B).9 C) D) -.9 9) Let logb A =.5 and logb B = 0.. Find logb AB. A).5 B).70 C) 0. D). 70) Let logb A =.09 and logb B = 0.. Find logb A B. A) 0.75 B).09 C). D).

25 7) Let logb = a and logb = c. Find logb b 5. A) b + a - 5 B) a + 5 C) ab D) (a + b) Use natural logarithms to evaluate the logarithm to the nearest thousandth. 7) log9 A).59 B) 0. C).59 D).7 7) log 0.5 A) B) 5.57 C) -. D) -0. 7) log7.9 9 A).0 B). C) 0.9 D).5 75) log.. A) 0.7 B) 0. C) 0. D).9 7) log 0. A) 0.0 B) 0.9 C).77 D)

26 Solve the equation. 77) log = log + log ( + 5) A) -0 B) 0 C) D) 7 7) log ( + 5) = log ( + ) A) - B) C) - D) 79) log = A) B) C).5 D) 9 0) log = A) B) / C) / D) ) log ( + ) - log ( - ) = log A) - B) C) D) No solution ) log7 (5 - ) = log7 ( + ) A) B) C) D) No solution

27 ) log ( + 5) = log ( + 7) A) - B) 5 7 C) 0 D) No solution ) log9 = log9 ( + ) A), - B) C) D) No solution 5) log = log A), 0 B) C) D) No solution Solve the equation. Round decimal answers to the nearest thousandth. ) = A).700 B).500 C).7 D) ) e -0.0 = 0.05 A) 9.77 B) -.5 C).99 D) ) e + = A) B) C) 0.07 D).9 7

28 9) ( - ) = A).5 B). C).00 D) ) e 5 + = A) -0.0 B).00 C) 0.0 D) ) e +9 = A) B) -0.7 C) D) -. 9) 00. = 90.9 A) -.9 B) 0. C) 0. D) Write the epression using base e rather than base 0. 9) A) 0e + 9 B) e (ln 0)( + 9) C) e0( + 9) D) ( + 9)e 0 9) 0 7 A) e (ln 0)7 B) 7 e 0 C) e 07 D) 0e 7

29 Approimate the epression in the form a without using e. Round to the nearest thousandth when necessar. 95) e A) B).7 C).079 D) ) e - A) 0. B) -0.7 C) 0.0 D) -. Find the domain of the function. 97) f() = log ( - ) A) > 0 B) > - C) > D) > 9) f() = ln (-5 - ) A) > -5 B) < -5 C) > 5 D) < 5 99) f() = log ( - ) A) - < < B) - < < C) - D) < - and > 00) f() = ln (7 - ) A) -7 < 0 B) 7 C) 0 < < 7 D) -7 < < 7 9

30 Solve the problem. 0) Sonja and Chris both accept new jobs on March, 00. Sonja starts at $,000 with a raise each March of %. Chris starts at $7,000 with a raise on March of each ear of %. In what ear will Chris' salar eceed Sonja's? A) 0 B) 09 C) 07 D) 0 0) A college student invests $000 in an account paing % per ear compounded annuall. In how man ears will the amount at least double? Round to the nearest tenth when necessar. A). r B). r C).9 r D) 9 r 0) How long will it take for prices in the econom to double at a % annual inflation rate? Round to the nearest hundredth when necessar. A).0 r B). r C) 7.7 r D).5 r 0) Assume the cost of a car is $7,000. With continuous compounding in effect, find the number of ears it would take to double the cost of the car at an annual inflation rate of %. Round to the nearest hundredth. A).55 r B) 7. r C) r D) 7. r 05) Suppose the consumption of electricit grows at % per ear, compounded continuousl. Find the number of ears before the use of electricit has tripled. Round to the nearest hundredth. A) 0. r B) 7.50 r C).7 r D).7 r 0) The purchasing power of a dollar is decreasing at the rate of % annuall, compounded continuousl. How long will it take for the purchasing power of $.00 to be worth $0.? Round to the nearest hundredth. A).55 r B) 9.00 r C) 5.5 r D) 0. r 0

31 07) At what interest rate must $00 be compounded annuall to equal $7.70 after ears? Round to the nearest percent. A) % B) 5% C) 7% D) % 0) Kimberl invested $000 in her savings account for 5 ears. When she withdrew it, she had $57.9. Interest was compounded continuousl. What was the interest rate on the account? Round to the nearest tenth of a percent when necessar. A) 7.05% B).9% C) 7% D).% 09) The magnitude of an earthquake, measured on the Richter scale, is given b R(I) = log I, where I is the I0 amplitude registered on a seismograph located 00 km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. Find the Richter scale rating of an earthquake with an amplitude of,09 I0. A). B) 0. C). D). 0) The magnitude of an earthquake, measured on the Richter scale, is given b R(I) = log I, where I is the I0 amplitude registered on a seismograph located 00 km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. An earthquake measured.5 on the Richter scale. Epress this reading in terms of I0. A) 5,9 I0 B) I0 C) 90 I0 D), I0

32 ) The magnitude of an earthquake, measured on the Richter scale, is given b R(I) = log I, where I is the I0 amplitude registered on a seismograph located 00 km from the epicenter of the earthquake, and I0 is the amplitude of a certain small size earthquake. Find the Richter scale rating of an earthquake with an amplitude of I0. A) 5.9 B) 5.9 C). D). ) A certain noise has intensit. 0 I0. What is the decibel rating of this sound? Use the formula D = 0 log I0, where I0 is a faint threshold sound, and I is the intensit of the sound. A) 0 decibels B) 9 decibels C) 9 decibels D) 79 decibels ) The ph of a solution is defined as ph = -log[h + ], where [H + ] is the concentration of hdrogen ions in the solution. The ph of pure water is 7, while the ph of lemon juice is about. How much greater is the concentration of hdrogen ions in lemon juice than in pure water? A) 5 times greater B) 0 times greater C) 00,000 times greater D) 0,000 times greater ) An RC circuit is a simple electronic circuit consisting of a resistor, a capacitor, and a batter. The current i in the circuit at some time t after the batter is connected is i = V R e-t/(rc), where V is the batter's voltage, R is the resistance, and C is the capacitance. Solve this equation for C. t A) C = R ln V ir B) C = Ve-t R C C) C = -R t ln ir V D) C = V R e-t/(ir)

33 5) One hundred rats are being trained to run through a maze and are rewarded when the run through it correctl. Once a rat successfull runs the maze, it continues to run the maze correctl in all subsequent trials. The number of rats that run the maze incorrectl after t attempts is given approimatel b N(t) = 00e -.t. Find the number of trials required such that onl 5% of the rats are running the maze incorrectl. Round to the nearest trial. A) 5 trials B) trials C) trials D) 7 trials ) The population growth of an animal species is described b F(t) = log (t + ) where t is measured in months. Find the population of this species in an area month(s) after the species is introduced. A) 00 B) 50 C) 90 D) 0 7) Cootes are one of the few species of North American animals with an epanding range. The future population of cootes in a region of Mississippi can be modeled b the equation P = 59 + ln(t + ), where t is time in ears. Use the equation to determine when the population will reach 0. (Round to the nearest tenth of a ear.) A). r B).5 r C). r D). r ) Find the effective rate corresponding to the nominal rate. % compounded monthl. Round to the nearest hundredth. A).% B).7% C).% D).% 9) Find the effective rate corresponding to the nominal rate. % compounded quarterl. Round to the nearest hundredth. A).0% B).09% C).% D).% 0) Find the present value of the deposit. $5000 at % compounded monthl for 5 ears. Round to the nearest cent. A) $5.0 B) $0.9 C) $095.0 D) $0.9

34 ) Find the present value of the deposit. $7000 at % compounded quarterl for ears. Round to the nearest cent. A) $55.7 B) $9. C) $57.7 D) $5. ) Find the present value of the deposit. $500 at 7% compounded continuousl for 0 ears. Round to the nearest dollar. A) $70 B) $0,90 C) $ D) $57 ) Find the present value of the deposit. $0,000 at % compounded continuousl for 0 ears. Round to the nearest dollar. A) $,9 B) $7,57 C) $7,57 D) $70 ) Barbara knows that she will need to bu a new car in 5 ears. The car will cost $5,000 b then. How much should she invest now at %, compounded quarterl, so that she will have enough to bu a new car? Round to the nearest cent. A) $0,57. B) $,.0 C) $,99. D) $,7.0 5) Southwest Dr Cleaners believes that it will need new equipment in ears. The equipment will cost $,000. What lump sum should be invested toda at % compounded semiannuall, to ield $,000? Round to the nearest cent. A) $,9.0 B) $,59. C) $,5. D) $,7.

35 ) An investment of $,5 earns % interest compounded monthl for ears. (a) What is the value of the investment after ears? (b) If mone can be deposited at % compounded quarterl, find the present value of the investment. Round to the nearest cent. A) (a) $5,5. (b) $,5. B) (a) $5,0. (b) $,. C) (a) $,0.0 (b) $,09.7 D) (a) $,0. (b) $5,5. 7) If mone can be invested at % compounded quarterl, which is larger -- $000 now or the present value of $0 left at % interest for 5 ears? A) $000 now B) Present value of $0 left for 5 ears ) A certificate of deposit pas 5% interest compounded quarterl. What effective interest rate does the CD pa? Round to the nearest tenth when necessar. A) 5.% B) 5.% C) % D).% 9) The sales of a new model of notebook computer are approimated b: S() = 000 -,000e -/9, where represents the number of months the computer has been on the market and S represents sales in thousands of dollars. In how man months will the sales reach $,00,000? Round to the nearest month. A) months B) months C) months D) 5 months 0) The sales of a mature product (one which has passed its peak) will decline b the function S(t)= S0e-at, where t is time in ears. Find the sales after ears if a = 0. and S0 = 0,700. Round to the nearest sale. A), sales B) 77 sales C) sales D) 79 sales 5

36 ) The number of books in a small librar increases according to the function B = 00e0.0t, where t is measured in ears. How man books will the librar have after ears? Round to the nearest book. A) 9 books B) 0 books C) 997 books D) 70 books ) In the formula N = Iekt, N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain countr to double if its annual growth rate is %? Round to the nearest ear. A) r B) 5 r C) r D) r ) In the formula N = Iekt, N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. How long will it take for the population of a certain countr to triple if its annual growth rate is 0.5%? Round to the nearest ear. A) 00 r B) 0 r C) r D) 95 r ) In the formula N = Iekt, N is the number of items in terms of an initial population I at a given time t and k is a growth constant equal to the percent of growth per unit time. There are currentl 7 million cars in a certain countr, increasing b.% annuall. How man ears will it take for this countr to have 0 million cars? Round to the nearest ear. A) r B) 9 r C) 7 r D) r 5) The number of acres in a landfill decreases according to the function B = 00e-0.0t, where t is measured in ears. How man acres will the landfill have after 5 ears? A),7 acres B) 5 acres C) 50 acres D) 9 acres

37 ) A bacteria colon doubles in 5 hr. How long does it take the colon to triple? Use N = N0 t/t, where N0 is the initial number of bacteria and T is the time in hours it takes the colon to double. (Round to the nearest hundredth, as necessar.) A) 5 hr B).0 hr C) 7.9 hr D) 7.5 hr 7) The population of a small countr increases according to the function B =,00,000e0.05t, where t is measured in ears. How man people will the countr have after 9 ears? A) 7,5 people B),75, people C),00, people D), people ) Use the formula P = Iekt. A bacterial culture has an initial population of 0,000. If its population declines to 5000 in hours, what will it be at the end of hours? A) 95 bacteria B) 5 bacteria C) 99 bacteria D) 500 bacteria 9) In the formula A(t) = A0ekt, A(t) is the amount of radioactive material remaining from an initial amount A0 at a given time t and k is a negative constant determined b the nature of the material. A certain radioactive isotope has a half-life of approimatel 950 ears. How man ears would be required for a given amount of this isotope to deca to 5% of that amount? A) 0 r B) r C) 07.5 r D) r 0) In the formula A(t) = A0ekt, A(t) is the amount of radioactive material remaining from an initial amount A0 at a given time t and k is a negative constant determined b the nature of the material. An artifact is discovered at a certain site. If it has 7% of the carbon- it originall contained, what is the approimate age of the artifact, rounded to the nearest ear? (carbon- decas at the rate of 0.05% annuall.) A) 00 r B) 590 r C) 09 r D) 0 r 7

38 ) In the formula A(t) = A0ekt, A(t) is the amount of radioactive material remaining from an initial amount A0 at a given time t and k is a negative constant determined b the nature of the material. A certain radioactive isotope decas at a rate of 0.% annuall. Determine the half-life of this isotope, to the nearest ear. A) r B) 7 r C) r D) 00 r ) The amount of particulate matter left in solution during a filtering process decreases b the equation P = 00()-0.n, where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.) A) 00, 75 B) 00, 75 C) 00, 9 D) 00, 00 ) The deca of 79 mg of an isotope is given b A(t)= 79e-0.0t, where t is time in ears. Find the amount left after 0 ears. A) mg B) mg C) mg D) 7 mg ) Newton's law of cooling states that the temperature f(t) of a bod at time t is given b: f(t) = T0 + Ce -kt, where C and k are constants and T0 is the temperature of the environment in which the object rests. If C = -.5 and k = 0.0 and t is in hours, how long will it take for a frozen roast to thaw to a temperature of 0 C in a refrigerator that is at 5 C? Round our answer to the nearest hour. A) hr B) hr C) hr D) hr 5) Newton's law of cooling states that the temperature f(t) of a bod at time t is given b: f(t) = T0 + Ce -kt, where C and k are constants and T0 is the temperature of the environment in which the object rests. If C = 0 and k = 0.7 and t is in minutes, how long will it take for a glass baking dish containing brownies to cool to a comfortable-to-touch temperature of 9 F in a room that is at 7 F? Round our answer to the nearest minute. A) 5 min B) 0 min C) 9 min D) min

39 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. ) f() = a The graph of an eponential function with base a is given. Sketch the graph of g() = -a. Give the domain and range of g. Answer: domain: (-, ), range: (-, 0) 9

40 7) f() = a The graph of an eponential function with base a is given. Sketch the graph of h() = a-. Give the domain and range of h. Answer: domain: (-, ), range: (0, ) ) Eplain how the graph of = can be obtained from the graph of =. Answer: The graph is shifted 5 units to the right and 5 units down. 9) Eplain how the graph of = (/) - can be obtained from the graph of =. Answer: The graph is reflected over the -ais and then shifted units down. 0

41 MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert the degree measure to radians. Leave the answer as a multiple of π. 50) 90 A) π B) π C) π D) π 5) -0 A) - π B) - π 5 C) - π 5) 570 5) 0 D) - π 7 A) 9π B) 9π C) 9π D) 9π 5 A) - 7π B) 7π C) - 7π D) 7π

42 5) 0 55) A) π 7 B) π C) 0π 5 D) 5 π A) 9π 0 B) π 5 5) 70 57) 70 C) 9π 5 D) π A) 7π 9 B) π C) 7π D) 7π A) 7 π B) 7 9 π C) π D) 7 π

43 Convert the radian measure to degrees. 5) π A) 90 B) 5 C).5 D).5 59) - π 0) π A) -0 B) -0 C) -0 D) -0 A) 90 B) 95 C) 990 D) 505 ) - 5π A) -5 B) -50 C) -5 D) -900 Find the indicated trigonometric function for θ, given that θ is an angle in standard position with the terminal side defined b the given point. ) (, ); find sin θ A) B) C) 5 D) 5

44 ) (, ); find cos θ A) B) C) 5 D) 5 ) (-5, ); find sin θ A) - B) C) 5 D) - 5 5) (-0, -); find cos θ A) - 5 B) 5 C) - D) - 5 ) (-0, ); find sec θ A) 5 B) - 5 C) - 5 D) -

45 7) (, ); find csc θ A) 5 B) C) 5 D) ) (5, -0); find csc θ A) 5 B) - 5 C) - 5 D) 5 9) (-, 9); find tan θ A) - B) - C) 9 D) - 70) (, ); find cot θ A) 9 B) 9 C) D) 5

46 If θ is an angle in the indicated quadrant, determine whether the given function is positive or negative. 7) II, sec θ A) Positive B) Negative 7) III, cot θ A) Positive B) Negative 7) IV, cot θ A) Negative B) Positive 7) II, sin θ A) Positive B) Negative 75) III, cos θ A) Negative B) Positive 7) IV, sin θ A) Positive B) Negative 77) II, tan θ A) Positive B) Negative 7) III, csc θ A) Negative B) Positive 79) IV, sec θ A) Negative B) Positive 0) I, csc θ A) Positive B) Negative

47 Give the eact value. ) cot 0 A) B) C) D) ) sin 0 A) B) C) D) ) cos 5 A) B) C) D) ) cos 0 A) B) - C) - D) 7

48 5) tan 00 A) B) - C) - D) ) cot 0 A) - B) - C) - D) 7) sec 0 A) B) - C) D) - ) sec 50 A) - B) C) - D) 9) csc 0 A) - B) C) - D)

49 90) csc 0 A) - B) - C) D) Find the eact value of the following epression without using a calculator. 9) csc π A) B) C) D) 9) sec π A) B) C) D) 9) cos π A) B) C) D) 9

50 9) sin 5π A) B) C) - D) - 95) cos π A) B) - C) - D) 9) tan 5π A) B) - C) D) - 97) csc 5π A) - B) - C) - D) - 50

51 9) sec 5π A) - B) C) - D) - 99) cot -π A) - B) C) D) - 00) sec(π) A) B) 0 C) - D) Undefined Find all values of between 0 and π that satisf the equation. 0) cos = A) π, π B) π, π C) π, 7π D) π, 5π 5

52 0) sin = A) π, 5π B) 5π, 7π C) π, 5π D) π, π 0) tan = A) 5π, π B) π, 7π C) π, 7π D) π, π 0) csc = A) π, 7π B) π, π C) π, 5π D) π, 5π 05) sec = - A) π, 5π B) π, 7π C) 5π, 7π D) π, π 5

53 Use a calculator to find the function value to four decimal places. 0) sin 7.9 A).505 B) C) D) ) cos 7. A) 0.57 B) 0.9 C) 0.59 D) ) cot 70.7 A) 0.50 B) C) 0.9 D) ) tan 7.7 A).0990 B) 0.9 C) 0.79 D) ) csc 75. A).0 B) -0.9 C) 0.9 D) 0.57 ) tan 59 A).05 B) -0.5 C) -. D) -.9 ) sin 0.0 A) 0.5 B) 0. C).0 D)

54 ) sec 0.5 A) 0.9 B) 0.5 C).0 D) 0.7 ) tan.95 A).07 B) -0.7 C) D) -.79 Give the amplitude or period as requested. 5) Amplitude of f() = sin A) π B) C) π D) π ) Amplitude of f() = - sin 5 A) π B) 5 C) π 5 D) 7) Period of f() = sin 5 A) π 5 B) C) 5 D) π 5

55 ) Amplitude of f() = cos A) π B) C) D) π 9) Period of f() = cos A) π B) π C) D) 0) Period of f() = cos A) B) π C) π D) π ) Period of f() = cos A) B) π C) π D) π ) Amplitude of f(t) = - cos π 7 t + 9 A) B) 9 C) - D) 55

56 ) Period of f(t) = cos π 5 t - A) 0π B) π 5 C) 5 D) 0 ) Period of f() = cos(7π + ) A) π 7 B) 7π C) 7 D) Graph the function. 5) = cos - - A) - - 5

57 B) - C) D)

58 ) =.5 sin - A) - - B) - - C)

59 D) - - 7) = tan - A)

60 B) - C) - - D)

61 ) = cos - A) - - B) - - C) - - -

62 D) - - 9) = -cos(π) A)

63 B) C) D)

64 0) = sin - A) - - B) - - C) - - -

65 D) - - ) = - cos + π A)

66 B) C) D)

67 ) = sin( + π) - - A) - - B) - - C) - - 7

68 D) - ) = 5 tan 5 + π - - A)

69 B) C) D)

70 ) = sin( - π) A) B)

71 C) 7 5 D) 7 5 Solve the problem. 5) Sales of snow shovels are seasonal. Suppose the sale of snow shovels in Maine is approimated b s(t) = 0, ,000 cos π t, where t is time in months and t = 0 is October. What are the sales in December? A) 5,000 snow shovels B),900 snow shovels C),0 snow shovels D) 7,07 snow shovels ) The temperature in Fairbanks is approimated b T() = 7 sin π ( - 0) + 5, where T() is the temperature 5 on da, with = corresponding to Jan and = 5 corresponding to Dec. Estimate the temperature, to the nearest degree, on da 5. A) - B) -5 C) D) -7 7

72 7) A scientist studing ocean tides places an ft high marker in the water at am on a Monda morning. At that time the water is about 5.5 ft high and receding. The scientist observes that the water reaches its lowest level, 0. ft, at 9: am and then begins to rise. Assume that the water level, in feet, is given b h(t) =.9 sin π. t + 5, where t represents the number of hours after midnight. (In other words, the marker was placed in the water when t =.) Find the first time interval during which the marker is completel underwater. A) Approimatel from : pm to 5: pm Monda B) Approimatel from : pm Monda to :00 am Tuesda C) Approimatel from : am to :5 am Tuesda D) Approimatel from :0 pm to : pm Monda ) The voltage E in an electrical circuit is given b E = 7. cos(0πt), where t is time measured in seconds. Find the period. A) 0 B) 0π C) 0 D) π 0 9) The total sales in dollars of some small businesses fluctuates according to the equation S = A + B sin π, where is the time in months, with = corresponding to Januar, A = 500, and B = 00. Determine the month with the greatest total sales and give the sales in that month. A) September; $00 B) December; $,700 C) June; $500 D) March; $,700 0) The total sales in dollars of some small businesses fluctuates according to the equation S = A + B sin π, where is the time in months, with = corresponding to Januar, A = 700, and B = 00. Determine the month with the least sales and give the sales in that month. A) December; $700 B) March; $0,500 C) June; $00 D) September; $900 7

73 ) The motion of a spring-mass sstem is described b the equation = 9 sin πt - π, where is the distance in feet from the equilibrium position and t is time in seconds. If the weight is feet from the ceiling in a state of equilibrium, find the time at which the weight first passes the equilibrium position. A) sec B) sec C) sec D) sec ) The motion of a spring-mass sstem is described b the equation = sin πt - π, where is the distance in feet from the equilibrium position and t is time in seconds. If the weight is feet from the ceiling in a state of equilibrium, find the closest the weight will ever be to the ceiling. A) ft B) ft C) 0 ft D) ft ) The motion of a spring-mass sstem is described b the equation = sin πt - π, where is the distance in feet from the equilibrium position and t is time in seconds. If the weight is feet from the ceiling in a state of equilibrium, find the distance from the ceiling at time t =. A) ft B) ft C) ft D) 0 ft ) The position of a weight attached to a spring is s(t) = - cos(πt) inches after t seconds. What is the maimum height that the weight reaches above the equilibrium position and when does it first reach the maimum height? A) The maimum height of inches is first reached after 0.0 seconds. B) The maimum height of inches is first reached after seconds. C) The maimum height of inches is first reached after seconds. D) The maimum height of inches is first reached after seconds. 7

74 5) The inde of refraction for air, Ia, is.000. The inde of refraction for water, Iw, is.. If I w Ia = sin A sin W, and A =.5, find W to the nearest tenth. A) 0.7 B).7 C).7 D).7 ) Snell's Law states that c c = sin θ sin θ. Use this law to find the requested value. If c = 7 0, θ =, and θ =, find c. A) c =.0 0 B) c =. 0 5 C) c =. 0 D) c =.5 0 7) Snell's Law states that c c = sin θ sin θ. Use this law to find the requested value. If c =. 0, θ = 57 and θ =, find c. A) c =.7 0 B) c = C) c = 0 D) c =. 0 0 ) Snell's Law states that c c = sin θ sin θ. Use this law to find the requested value. If c = 0 7, c =.7 0 7, θ =, find θ. Round our answer to the nearest degree. A) θ = 5 B) θ = C) θ = D) θ = 7

75 9) Snell's Law states that c c = sin θ sin θ. Use this law to find the requested value. If c = 7 0, c = 5.5 0, θ =, find θ. Round our answer to the nearest degree. A) θ = 9 B) θ = 5 C) θ = D) θ = 50) From a boat on the lake, the angle of elevation to the top of a cliff is 9'. If the base of the cliff is 9 feet from the boat, how high is the cliff (to the nearest foot)? A) 7 ft B) 75 ft C) 7 ft D) 75 ft 5) From a boat on the river below a dam, the angle of elevation to the top of the dam is '. If the dam is 7 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)? A) 0 ft B) 0 ft C) 09 ft D) 07 ft 5) From a balloon 7 feet high, the angle of depression to the ranger headquarters is 7 '. How far is the headquarters from a point on the ground directl below the balloon (to the nearest foot)? A) 57 ft B) ft C) 5 ft D) 7 ft 5) When sitting atop a tree and looking down at his pal Joe, the angle of depression of Mack's line of sight is '. If Joe is known to be standing 0 feet from the base of the tree, how tall is the tree (to the nearest foot)? A) 0 ft B) ft C) ft D) ft 5) The air speed of an airplane is 90 km/hr and its angle of climb is.07. What is its ground speed (to the nearest km/hr)? A) 90 km/hr B) 5 km/hr C) 75 km/hr D) 0 km/hr 75

76 55) At an altitude of 500 ft, the engine on a small plane fails. What angle of glide is needed to reach an airport runwa that is miles awa b land? (Round our answer to the nearest tenth of a degree.) A).9 B) 0. C) 9. D) 9.9 5) The chairlift at a ski resort has a vertical rise of 00 feet. If the length of the ride is. miles, what is the average angle of inclination of the lift (to the nearest tenth of a degree)? A) 9. B) 5. C). D). 57) A 0-foot ladder is leaning against the side of a building. If the ladder makes an angle of with the side of the building, how far is the bottom of the ladder from the base of the building? Round our answer to the hundredths place. A). ft B).5 ft C).9 ft D).9 ft 5) A contractor needs to know the height of a building to estimate the cost of a job. From a point 9 feet awa from the base of the building, the angle of elevation to the top of the building is found to be 5. Find the height of the building. Round our answer to the hundredths place. A) 9.7 ft B) 90.ft C) 9.5 ft D) 95. ft 7

77 59) A conservation officer needs to know the width of a river in order to set instruments correctl for a stud of pollutants in the river. From point A, the conservation officer walks 90 feet downstream and sights point B on the opposite bank to determine that θ = 0 (see figure). How wide is the river? θ = 0 A) 0 ft B) 7 ft C) 5 ft D) 5 ft 90 ft. 0) A weight attached to a spring is pulled down inches below the equilibrium position. Assuming that the period of the sstem is 5 second, determine a trigonometric model that gives the position of the weight at time t seconds. A) = cos 5 t B) = cos 0πt C) = - cos 5πt D) = - cos 0πt ) A weight attached to a spring is pulled down inches below the equilibrium position. Assuming that the frequenc of the sstem is 5 π ccles per second, determine a trigonometric model that gives the position of the weight at time t seconds. A) = cos 0t B) = - cos 0t C) = cos 5t D) = - cos 5t 77

78 Calculus for the Life Sciences nd Edition Greenwell Test Bank Full Download: ) Tides go up and down in a -hour period. The average depth of a certain river is m and ranges from to 7 m. The depth of the river can be approimated b a sine curve. Write an equation that gives the depth hours after midnight given that high tide occurs at 7:00 am. A) d = sin π 7 - π + B) d = sin π 7 + C) d = 7 sin π 7 - π D) d = sin π - π + 7 Full download all chapters instantl please go to Solutions Manual, Test Bank site: testbanklive.com