Test Bank for Calculus for the Life Sciences, 2nd Edition

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Match the graph to the function. 1) 1) _______ A) f(x) = + 1 B) f(x) = – 1 C) f(x) = D) f(x) = 2) 2) _______ A) f(x) = 3) B) f(x) = C) f(x) = D) f(x) = 3) _______ A) f(x) = B) f(x) = – C) f(x) = D) f(x) = – 4) 4) _______ A) f(x) = – B) f(x) = C) f(x) = D) f(x) = – 5) 5) _______ A) f(x) = 6) B) f(x) = C) f(x) = D) f(x) = – 6) _______ A) f(x) = -3 B) f(x) = 3 C) f(x) = 3 D) f(x) = -3 7) 7) _______ A) f(x) = – 2 B) f(x) = C) f(x) = D) f(x) = +2 8) 8) _______ A) f(x) = B) f(x) = + 2 C) f(x) = D) f(x) = -2 9) 9) _______ A) y = B) y = C) y = D) y = 10) 10) ______ A) y = – 2B) y = -2 Solve the equation. 11) 4x = 64 11) ______ A) 2 B) 4 C) 3 D) 16 12) = 12) ______ A) -3 B) C) D) 3 13) 3(12 – 3x) = 729 13) ______ A) 4 B) -2 C) 243 D) 2 14) 3(1 + 2x) = 27 A) -1 B) 9 C) 3 14) ______ D) 1 C) y = – 2 D) y = -2 15) 4(7 – 3x) = 15) ______ A) 4 B) C) 3 16) = 16) ______ A) -3 B) C) 17) 4(7 + 3x) = A) 3 B) -3 18) = A) B) 19) D) -3 D) 3 17) ______ C) 4 D) 18) ______ C) 0 = D) – 19) ______ A) 2, -2 B) 3, -3 C) 3 D) 1, -1 Graph the function. 20) y = 4 -1 20) ______ A) B) C) D) 21) y = -4 -4 21) ______ A) B) C) D) 22) y = 5 +3 22) ______ A) B) C) D) 23) y = 2 -3 23) ______ A) B) C) D) 24) y = -2 +3 24) ______ A) B) C) D) Solve the problem. 25) Find the amount of interest earned on the following deposit: $1000 at 6% compounded annually for 8 years ______ A) $689.48 B) $1593.85 C) $503.63 25) D) $593.85 26) How long will it take for prices in the economy to double at a 5% annual inflation rate? Round to the nearest hundredth when necessary. 26) ______ A) 11.9 yr B) 14.21 yr C) 23.45 yr D) 22.52 yr 27) An economist predicts that the buying power B(x) of a dollar x years from now will decrease according to the formula B(x) = 0.46x. How much will today’s dollar be worth in 3 years? Round to the nearest cent. 27) ______ A) $1.38 B) $0.10 C) $1.66 D) $0.79 28) Find the interest earned on cent. 28) ______ A) $15,334.74 B) $1987.77 invested for 5 years at C) $1.39 D) $4334.74 29) Find the interest earned on cent. 29) ______ A) $4355.80 B) $4518.69 interest compounded quarterly. Round to the nearest invested for 6 years at C) $4528.02 interest compounded monthly. Round to the nearest D) $4487.93 30) Suppose that the number of bacteria in a culture after x hours is given by in the culture after 10 hours? 30) ______ A) 13,133 bacteria C) 828,614 bacteria B) 7477 bacteria D) 3 bacteria 31) Suppose that the number of bacteria in a culture after x hours is given by the culture after 4 hours? 31) ______ A) 18,000 bacteria . How many bacteria are B) 39 bacteria . How many bacteria are in C) 1661 bacteria D) 134 bacteria 32) The population of a particular city is increasing at a rate proportional to its size. It follows the function P(t) = 1 + ke0.04t where k is a constant and t is the time in years. If the current population is 37,000, in how many years is the population expected to be 92,500? 32) ______ A) 13 yr B) 10 yr C) 23 yr D) 147 yr 33) The number of dislocated electric impulses per cubic inch in a transformer increases when lightning strikes by D = 9200(5)x, where x is the time in milliseconds of the lightning strike. Find the number of dislocated impulses at x = 0 and x = 4. 33) ______ A) 46,000; 5,750,000 B) 9200; 5,750,000 C) 9200; 184,000 D) 9200; 28,750,000 34) The number of bacteria growing in an incubation culture increases with time according to where x is time in days. Find the number of bacteria when x = 0 and x = 4. A) 7800 bacteria, 4,875,000 bacteria C) 39,000 bacteria, 4,875,000 bacteria 34) ______ B) 7800 bacteria, 156,000 bacteria D) 7800 bacteria, 24,375,000 bacteria 35) The number of books in a small library increases according to the function B = 5400e 0.02t, where t is measured in years. How many books will the library have after 9 years? 35) ______ A) 4022 books B) 8173 books C) 6465 books D) 9260 books Write the exponential equation in logarithmic form. 36) 72 = 49 36) ______ A) log7 49 = 2 B) log2 49 = 7 C) log7 2 = 49 D) log49 7 = 2 37) 42 = 16 A) log4 16 = 2 37) ______ B) log2 16 = 4 C) log4 2 = 16 D) log16 4 = 2 38) 4-2 = 38) ______ A) log1/16 4 = -2 B) log4 -2 = C) log-2 39) = A) (-2) = B) = -2 C) (-2) = D) = -2 = 4 D) log4 = -2 39) ______ Write the logarithmic equation in exponential form. 40) log4 A) = -2 =4 40) ______ B) 24 = 41) log2 8 = 3 41) ______ A) 32 = 8 B) 83 = 2 42) log 0.00001 = -5 A) 0.00001-5 = 10 43) A) C) 416 = 2 D) 4-2 = C) 28 = 3 D) 23 = 8 42) ______ B) -510 = 0.00001 C) 10-5 = 0.00001 16 = 4 43) ______ = 16 B) = C) =4 D) = 16 + 1 D) 100.00001 = -5 44) log 100 = 2 44) ______ A) = 100 B) = 45) ln x = 7 45) ______ A) B) =x =e 46) ln = -6 46) ______ A) = -6 B) 47) ln =8 47) ______ A) ln 8 = 8 48) ln A) B) = = = =8 C) =2 D) = 1000 C) =x D) =7 C) = D) C) ln = D) C) = D) B) ln B) 4 50) log4 A) 0 = 51) log7 A) 7 C) 3 D) 12 50) ______ B) -1 C) 1 D) 4 51) ______ B) -2 C) 2 D) -7 52) log10 10 52) ______ A) 1 C) 0 B) -1 D) 10 53) log9 53) ______ A) -81 B) 3 C) -3 54) log8 32 54) ______ A) C) B) = 48) ______ Evaluate the logarithm without using a calculator. 49) log4 64 49) ______ A) 64 =e D) 81 D) = 55) ln e 55) ______ A) 1 B) 0 C) -1 D) e 56) ln l 56) ______ A) -1 B) e C) 0 D) 1 57) 57) ______ A) – 2 B) 2 C) – D) 58) ln 58) ______ A) C) e B) D) e Rewrite the expression as a sum, difference, or product of simpler logarithms. 59) log8 11x 59) ______ A) log8 11 – log8 x 60) log6 xy B) log3 x – log3 y B) log4 9 – log4 10 log2 6 – log2 11 B) log4 11 – C) log4 6 + log4 11 D) 63) 63) ______ C) 3p – C) log6 x + log6 y D) log6 x – log6 y C) log4 9 + log4 10 D) log4 10 – log4 9 62) ______ A) A) D) log4 11 – log4 x 61) ______ A) log2 9 – log2 10 62) log4 C) log4 11 + log4 x 60) ______ A) log3 x + log3 y 61) log4 B) log8 11 + log8 x 5k log4 6 log4 6 – log4 11 B) D) 3+ p-1- k 64) A) 64) ______ 2+ 6- C) 3 B) 2+5 6-4 3 D) Use the properties of logarithms to find the value of the expression. 65) Let logb A = 2 and logb B = -3. Find logb AB. 65) ______ A) -6 B) 6 C) -1 D) 5 66) Let logb A = 4 and logb B = -20. Find logb A) -16 B) C) 24 . 66) ______ D) – 67) Let logb A = 3 and logb B = -4. Find logb B2. 67) ______ A) 6 B) -16 C) -8 D) 16 68) Let logb A = 3 and logb B = -2. Find logb 2 A) -2.449 . 68) ______ B) 0.500 C) 2.449 D) 2 69) Let logb A = 2.518 and logb B = 0.186. Find logb AB. 69) ______ A) 2.332 B) 13.538 C) 0.468 D) 2.704 70) Let logb A = 3.098 and logb B = 0.234. Find logb A) 2.864 . 70) ______ B) 0.725 C) 3.098 D) 3.332 71) Let logb 6 = a and logb 3 = c. Find logb A) 3ab B) 3(a + b) C) 3b + a – 5 . 71) ______ D) 3a + 5 Use natural logarithms to evaluate the logarithm to the nearest thousandth. 72) log9 33 72) ______ A) 3.667 B) 1.591 C) 1.519 D) 0.628 73) log2 0.358 73) ______ A) -0.446 B) -1.482 74) log7.9 192 74) ______ A) 2.283 B) 0.393 C) 24.304 C) 5.587 D) -0.675 D) 2.544 75) log3.4 2.3 75) ______ A) 1.469 B) 0.681 C) 0.676 D) 0.362 76) log A) 0.106 180.1 76) ______ B) 9.455 C) 4.727 D) 0.239 Solve the equation. 77) log 3x = log 2 + log (x + 5) A) B) 10 C) -10 D) 2 78) log (x + 5) = log (2x + 3) A) 8 B) – C) -2 78) ______ D) 2 79) log2 x = 3 79) ______ A) 8 C) 1.58 D) 6 B) 9 77) ______ 80) logy 13 = 2 80) ______ A) 132 B) 131/2 C) D) 21/13 81) log (3 + x) – log (x – 4) = log 2 81) ______ A) B) 11 C) -11 D) No solution 82) log7 (5x – 3) = log7 (2x + 6) A) 3 B) 3 C) 1 D) No solution 83) log8 (6x + 5) = log8 (6x + 7) A) B) – 6 C) 0 82) ______ 83) ______ D) No solution 84) log9 x2 = log9 (4x + 12) 84) ______ A) 6, -2 D) No solution B) C) 6 85) log2 x2 = log4 4x 85) ______ A) 4 B) 8 C) 4, 0 D) No solution Solve the equation. Round decimal answers to the nearest thousandth. 86) = 13 A) 1.872 87) 86) ______ B) 3.700 C) 6.500 D) 0.270 = 0.05 87) ______ A) 2.996 B) -2.5 C) -149.787 88) =2 A) -7.699 88) ______ B) -7.307 D) 149.787 C) 0.087 D) 8.693 89) A) 1.004 = 11 89) ______ B) -0.090 C) 1.583 D) 1.243 90) 6 A) 0.020 = 18 90) ______ B) -0.104 C) 0.420D) 3.400 91) A) -4.507 = 2 91) ______ B) -0.687 C) -3.813 D) -2.597 92) 10 =9 92) ______ A) -8.96 B) 0.21 C) 0.164D) 0.000 Write the expression using base e rather than base 10. 93) 93) ______ A) 10 B) 94) 94) ______ A) B) C) C) 10 D) Approximate the expression in the form 95) 95) ______ A) B) 96) 96) ______ A) B) D) (x + 9) without using e. Round to the nearest thousandth when necessary. C) D) C) D) Find the domain of the function. 97) f(x) = log (x – 6) 97) ______ A) x > 0 B) x > 6 C) x > -6 D) x > 1 98) f(x) = ln (-5 – x) 98) ______ A) x -5C) x > 5 D) x < 5 99) f(x) = log8 (4 – x2) A) -2 ≤ x ≤ 2 99) ______ B) x 2 C) -2 < x < 2 D) -4 < x < 4 100) f(x) = ln (7x – x2) 100) _____ A) -7 < x < 7 B) -7 ≤ x < 0 C) x ≤ 7 D) 0 < x < 7 Solve the problem. 101) Sonja and Chris both accept new jobs on March 1, 2001. Sonja starts at Chris starts at with a raise on March 1 of each year of with a raise each March 1 of . . In what year will Chris' salary exceed Sonja's? 101) _____ A) 2019 B) 2018 C) 2016 D) 2017 102) A college student invests $8000 in an account paying per year compounded annually. In how many years will the amount at least double? Round to the nearest tenth when necessary. 102) _____ A) 16.3 yr B) 9 yr C) 11.9 yr D) 14.3 yr 103) How long will it take for prices in the economy to double at a 4% annual inflation rate? Round to the nearest hundredth when necessary. 103) _____ A) 23.45 yr B) 17.67 yr C) 14.21 yr D) 28.01 yr 104) Assume the cost of a car is $27,000. With continuous compounding in effect, find the number of years it would take to double the cost of the car at an annual inflation rate of 4%. Round to the nearest hundredth. 104) _____ A) 17.33 yr B) 272.42 yr C) 2.55 yr D) 255.09 yr 105) Suppose the consumption of electricity grows at 8% per year, compounded continuously. Find the number of years before the use of electricity has tripled. Round to the nearest hundredth. 105) _____ A) 1.37 yr B) 13.73 yr C) 37.50 yr D) 0.14 yr 106) The purchasing power of a dollar is decreasing at the rate of 4% annually, compounded continuously. How long will it take for the purchasing power of $1.00 to be worth $0.36? Round to the nearest hundredth. 106) _____ A) 2.55 yr B) 25.54 yr C) 9.00 yr D) 0.26 yr 107) At what interest rate must $4400 be compounded annually to equal $8711.70 after 14 years? Round to the nearest percent. 107) _____ A) 7% B) 4% C) 5% D) 6% 108) Kimberly invested in her savings account for 5 years. When she withdrew it, she had . Interest was compounded continuously. What was the interest rate on the account? Round to the nearest tenth of a percent when necessary. 108) _____ A) 6.8% B) 7% C) 6.9% D) 7.05% 109) The magnitude of an earthquake, measured on the Richter scale, is given by registered on a seismograph located 100 km from the epicenter of the earthquake, and where I is the amplitude is the amplitude of a certain small size earthquake. Find the Richter scale rating of an earthquake with an amplitude of 63,096 . 109) _____ A) 3.8 B) 0.48 C) 11.1 D) 4.8 110) The magnitude of an earthquake, measured on the Richter scale, is given by registered on a seismograph located 100 km from the epicenter of the earthquake, and where I is the amplitude is the amplitude of a certain small size earthquake. An earthquake measured 4.5 on the Richter scale. Express this reading in terms of _____ A) 25,119 B) 90 C) 31,623 registered on a seismograph located 100 km from the epicenter of the earthquake, and where I is the amplitude is the amplitude of a certain small size earthquake. Find the Richter scale rating of an earthquake with an amplitude of . 111) _____ C) 13.6 D) 4.1 112) A certain noise has intensity 8.62 × where 110) D) 3162 111) The magnitude of an earthquake, measured on the Richter scale, is given by A) 15.9 B) 5.9 . . What is the decibel rating of this sound? Use the formula is a faint threshold sound, and I is the intensity of the sound.” 112) _____ A) 9 decibels B) 79 decibels C) 89 decibels D) 206 decibels 113) The pH of a solution is defined as pH = -log[ ], where [ ] is the concentration of hydrogen ions in the solution. The pH of pure water is 7, while the pH of lemon juice is about 2. How much greater is the concentration of hydrogen ions in lemon juice than in pure water? 113) _____ A) 10,000 times greater B) 5 times greater C) 10 times greater D) 100,000 times greater 114) An RC circuit is a simple electronic circuit consisting of a resistor, a capacitor, and a battery. The current i in the circuit at some time t after the battery is connected is i = , where V is the battery's voltage, R is the resistance, and C is the capacitance. Solve this equation for C. 114) _____ A) C = B) C = C) C = D) C = 115) One hundred rats are being trained to run through a maze and are rewarded when they run through it correctly. Once a rat successfully runs the maze, it continues to run the maze correctly in all subsequent trials. The number of rats that run the maze incorrectly after t attempts is given approximately by Find the number of trials required such that only 45% of the rats are running the maze incorrectly. Round to the nearest trial. 115) _____ A) 23 trials B) 6 trials C) 5 trials D) 27 trials 116) The population growth of an animal species is described by where t is measured in months. Find the population of this species in an area 1 month(s) after the species is introduced. 116) _____ A) 380 B) 200 C) 290 D) 540 117) Coyotes are one of the few species of North American animals with an expanding range. The future population of coyotes in a region of Mississippi can be modeled by the equation , where t is time in years. Use the equation to determine when the population will reach 140. (Round to the nearest tenth of a year.) 117) _____ A) 8248.4 yr B) 11.5 yr C) 11.2 yr D) 11.4 yr 118) Find the effective rate corresponding to the nominal rate. 6% compounded monthly. Round to the nearest hundredth. 118) _____ A) 6.26% B) 6.23% C) 6.17% D) 6.12% 119) Find the effective rate corresponding to the nominal rate. 6% compounded quarterly. Round to the nearest hundredth. 119) _____ A) 6.23% B) 6.14% C) 6.09% D) 6.20% 120) Find the present value of the deposit. $5000 at 4% compounded monthly for 5 years. Round to the nearest cent. 120) _____ A) $6084.98 B) $4115.02 C) $4095.02 D) $6104.98 121) Find the present value of the deposit. $7000 at 6% compounded quarterly for 3 years. Round to the nearest cent. 121) _____ A) $5872.71 B) $8351.33 C) $5854.71 D) $8369.33 122) Find the present value of the deposit. $500 at 7% compounded continuously for 10 years. Round to the nearest dollar. 122) _____ A) $248 B) $10,690 C) $3547 D) $7240 123) Find the present value of the deposit. $10,000 at 4% compounded continuously for 10 years. Round to the nearest dollar. 123) _____ A) $167,587 B) $122,941 C) $6703 D) $417,587 124) Barbara knows that she will need to buy a new car in 5 years. The car will cost $15,000 by then. How much should she invest now at 6%, compounded quarterly, so that she will have enough to buy a new car? Round to the nearest cent. 124) _____ A) $12,939.13 B) $11,137.06 C) $11,881.40 D) $10,574.41 125) Southwest Dry Cleaners believes that it will need new equipment in 6 years. The equipment will cost $26,000. What lump sum should be invested today at 6% compounded semiannually, to yield $26,000? Round to the nearest cent. 125) _____ A) $18,235.88 B) $21,894.60 C) $23,593.24 D) $21,731.62 126) An investment of $13,335 earns 8% interest compounded monthly for 2 years. (a) What is the value of the investment after 2 years? (b) If money can be deposited at 6% compounded quarterly, find the present value of the investment. Round to the nearest cent. 126) _____ A) (a) $15,640.46 (b) $13,884.21 B) (a) $15,536.88 (b) $14,518.42 C) (a) $16,640.46 (b) $15,518.42 (b) $14,092.47 D) (a) $14,063.02 127) If money can be invested at 6% compounded quarterly, which is larger — $1000 now or the present value of $1210 left at 6% interest for 5 years? 127) _____ A) $1000 now B) Present value of $1210 left for 5 years 128) A certificate of deposit pays interest compounded quarterly. What effective interest rate does the CD pay? Round to the nearest tenth when necessary. 128) _____ A) 5.1% B) 5.8% C) 21.6% D) 4% 129) The sales of a new model of notebook computer are approximated by: , where x represents the number of months the computer has been on the market and S represents sales in thousands of dollars. In how many months will the sales reach $2,200,000? Round to the nearest month. 129) _____ A) 21 months B) 25 months C) 28 months D) 18 months 130) The sales of a mature product (one which has passed its peak) will decline by the function S(t)= time in years. Find the sales after 11 years if a = 0.24 and A) 739 sales B) 1477 sales C) 1162 sales = 20,700. Round to the nearest sale. e-at, where t is 130) _____ D) 16,283 sales 131) The number of books in a small library increases according to the function B = 2100e 0.03t, where t is measured in years. How many books will the library have after 8 years? Round to the nearest book. 131) _____ A) 3649 books B) 2997 books C) 1302 books D) 2670 books 132) 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 country to double if its annual growth rate is 6%? Round to the nearest year. 132) _____ A) 33 yr B) 5 yr C) 12 yr D) 1 yr 133) 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 country to triple if its annual growth rate is 0.5%? Round to the nearest year. 133) _____ A) 1 yr B) 600 yr C) 95 yr D) 220 yr 134) 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 currently 73 million cars in a certain country, increasing by 3.8% annually. How many years will it take for this country to have 101 million cars? Round to the nearest year. 134) _____ A) 4 yr B) 7 yr C) 88 yr D) 9 yr 135) The number of acres in a landfill decreases according to the function B = 6200e -0.03t, where t is measured in years. How many acres will the landfill have after 5 years? 135) _____ A) 11,762 acres B) 5336 acres C) 5108 acres D) 4389 acres 136) A bacteria colony doubles in 5 hr. How long does it take the colony to triple? Use N = N 0 2t/T, where N0 is the initial number of bacteria and T is the time in hours it takes the colony to double. (Round to the nearest hundredth, as necessary.) 136) _____ A) 7.92 hr B) 7.5 hr C) 2.03 hr D) 15 hr 137) The population of a small country increases according to the function B = 1,100,000e 0.05t, where t is measured in years. How many people will the country have after 9 years? 137) _____ A) 3,100,221 people C) 1,725,143 people B) 878,358 people D) 381,466 people 138) Use the formula P = Iekt. A bacterial culture has an initial population of 10,000. If its population declines to 5000 in 6 hours, what will it be at the end of 8 hours? 138) _____ A) 2500 bacteria B) 1985 bacteria C) 3969 bacteria D) 4353 bacteria 139) In the formula A(t) = ekt, A(t) is the amount of radioactive material remaining from an initial amount at a given time t and k is a negative constant determined by the nature of the material. A certain radioactive isotope has a half-life of approximately 1950 years. How many years would be required for a given amount of this isotope to decay to 45% of that amount? 139) _____ A) 1682 yr B) 2201 yr C) 2246 yr D) 1072.5 yr 140) In the formula A(t) = ekt, A(t) is the amount of radioactive material remaining from an initial amount at a given time t and k is a negative constant determined by the nature of the material. An artifact is discovered at a cert ain site. If it has 74% of the carbon-14 it originally contained, what is the approximate age of the artifact, rounded to the nearest year? (carbon-14 decays at the rate of 0.0125% annually.) 140) _____ A) 1046 yr B) 2080 yr C) 5920 yr D) 2409 yr 141) In the formula A(t) = ekt, A(t) is the amount of radioactive material remaining from an initial amount at a given time t and k is a negative constant determined by the nature of the material. A certain radioactive isotope decays at a rate of 0.3% annually. Determine the half-life of this isotope, to the nearest year. 141) _____ A) 2 yr B) 231 yr C) 167 yr D) 100 yr 142) The amount of particulate matter left in solution during a filtering process decreases by the equation where n is the number of filtering steps. Find the amounts left for n = 0 and n = 5. (Round to the nearest whole number.) 142) _____ A) 600, 4800 B) 1200, 75 C) 600, 19 D) 600, 75 143) The decay of 279 mg of an isotope is given by A(t)= 279e -0.012t, where t is time in years. Find the amount left after 60 years. 143) _____ A) 276 mg B) 136 mg C) 134 mg D) 68 mg 144) Newton's law of cooling states that the temperature f(t) of a body at time t is given by: where C and k are constants and is the temperature of the environment in which the object rests. If C = -28.5 and k = 0.04 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 your answer to the nearest hour. 144) _____ A) 48 hrB) 38 hr C) 42 hr D) 44 hr 145) Newton's law of cooling states that the temperature f(t) of a body at time t is given by: where C and k are constants and is the temperature of the environment in which the object rests. If C = 280 and k = 0.17 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 93°F in a room that is at 72°F? Round your answer to the nearest minute. 145) _____ A) 19 min B) 15 min C) 10 min D) 12 min SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 146) f(x) = ax The graph of an exponential function with base a is given. Sketch the graph of g(x) = -ax. Give the domain and range of g. 146) ____________ 147) f(x) = ax The graph of an exponential function with base a is given. Sketch the graph of h(x) = a -x. Give the domain and range of h. 147) ____________ 148) Explain how the graph of y = 3x – 5 – 5 can be obtained from the graph of y = 3x. 149) Explain how the graph of y = – 3 can be obtained from the graph of y = 2x. 148) ____________ 149) ____________ 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. 150) 90° 150) _____ A) B) C) D) 151) -30° 151) _____ A) – C) – B) – D) – 152) 570° 152) _____ A) C) B) D) 153) 630° 153) _____ A) 7π C) – B) D) – 154) 330° 154) _____ A) C) B) D) 155) 162° 155) _____ A) C) π B) D) 156) 470° 156) _____ A) B) 157) 370° 157) _____ A) πB) π C) π C) π D) π Convert the radian measure to degrees. 158) 158) _____ A) 90° B) 45° C) 32.5° D) 22.5° D) 159) – 159) _____ A) -30° B) -60° C) -40° D) -120° 160) 160) _____ A) 495° B) 1980°C) 990° D) 505° 161) – 161) _____ A) -900°B) -225° C) -450° D) -235° Find the indicated trigonometric function for θ, given that θ is an angle in standard position with the terminal side defined by the given point. 162) (18, 24); find sin θ 162) _____ A) B) C) D) 163) (12, 16); find cos θ163) _____ A) B) C) D) 164) (-15, 36); find sin θ A) – B) – C) D) 165) (-20, -48); find cos θ A) – B) – C) – B) – C) 165) _____ D) 166) (-10, 24); find sec θ A) – 164) _____ 166) _____ D) – 167) (21, 28); find csc θ 167) _____ A) B) C) D) 168) (15, -20); find csc θ A) – B) C) 168) _____ D) – 169) (-6, 9); find tan θ 169) _____ A) – B) – C) – D) 170) (4, 8); find cot θ 170) _____ A) D) B) C) 2 If θ is an angle in the indicated quadrant, determine whether the given function is positive or negative. 171) II, sec θ 171) _____ A) Negative B) Positive 172) III, cot θ A) Positive 172) _____ B) Negative 173) IV, cot θ A) Positive 173) _____ B) Negative 174) II, sin θ A) Positive 174) _____ B) Negative 175) III, cos θ A) Positive 175) _____ B) Negative 176) IV, sin θ A) Positive 176) _____ B) Negative 177) II, tan θ A) Positive 177) _____ B) Negative 178) III, csc θ A) Positive 178) _____ B) Negative 179) IV, sec θ A) Positive 179) _____ B) Negative 180) I, csc θ A) Negative 180) _____ B) Positive Give the exact value. 181) cot 30° 181) _____ A) 1 B) C) D) 182) sin 60° 182) _____ A) C) B) D) 183) cos 45° 183) _____ A) C) B) 184) cos 210° D) 184) _____ A) – B) 185) tan 300° 185) _____ A) – B) 186) cot 120° 186) _____ A) C) – B) -1 C) – C) – D) D) – 187) sec 240° 187) _____ A) – B) 188) sec 150° 188) _____ A) B) 189) csc 240° 189) _____ A) -2 C) – B) 2 D) C) -2 D) 2 C) – D) – D) 190) csc 330° 190) _____ A) – B) -2 C) 2 D) Find the exact value of the following expression without using a calculator. 191) csc 191) _____ A) B) 192) sec 192) _____ A) B) 193) cos A) C) 2 C) D) 193) _____ B) C) D) D) 2 194) sin A) 194) _____ B) – 195) cos A) 196) tan 197) csc D) – C) D) – 197) _____ B) – 198) sec A) – C) – 196) _____ B) A) – D) 195) _____ B) A) – C) – C) – D) – 198) _____ B) – C) D) -2 199) cot 199) _____ A) – B) 200) sec(π) A) -1 B) 0 200) _____ C) 1 D) Undefined C) – D) Find all values of x between 0 and 2π that satisfy the equation. 201) cos x = 201) _____ A) B) , , C) , D) , 202) sin x = 202) _____ A) B) , , C) 203) tan x = 203) _____ A) B) , , 204) csc x = 2 204) _____ A) B) , , 205) sec x = – 205) _____ A) B) , , , D) , C) , D) C) , D) , D) , C) , , Use a calculator to find the function value to four decimal places. 206) sin 72.9° 206) _____ A) 0.9558 B) 0.2940 C) 3.2505 D) -0.5999 207) cos 27.2° A) 0.8894 207) _____ B) 0.5139 C) 0.4571 D) -0.4763 208) cot 70.7° A) 2.8555 208) _____ B) 0.9438 C) 0.3502 D) -70.5904 209) tan 47.7° A) 0.7396 209) _____ B) 0.6496 C) 1.0990 D) 0.9099 210) csc 75.1° A) 0.2571 210) _____ B) 0.9664 C) -0.2938 D) 1.0348 211) tan 459° A) -0.1564 211) _____ B) 2.6051 C) -6.3138 D) -1.2349 212) sin 0.1630 212) _____ A) 0.1645 B) 1.0134 C) 0.9867 D) 0.1623 213) sec 0.56 A) 0.5312 213) _____ B) 0.6269 C) 1.1803 D) 0.8473 214) tan 3.95 A) -1.4479 214) _____ B) 1.0471 C) -0.6907 D) -0.7232 Give the amplitude or period as requested. 215) Amplitude of f(x) = 3 sin x 215) _____ A) B) 2π C) 3π D) 3 216) Amplitude of f(x) = -3 sin 5x A) B) C) D) 3 217) Period of f(x) = sin 5x A) B) 1 C) 2π B) 4 C) 217) _____ D) 5 218) Amplitude of f(x) = A) cos 4x B) 1 C) B) 4π C) 219) _____ D) 2π 220) Period of f(x) = 4 cos A) x B) C) 2π 220) _____ D) 4 221) Period of f(x) = 3 cos x A) 3 221) _____ D) π 222) Amplitude of f(t) = -2 cos A) -2 B) 14 C) 9 B) C) 2 Graph the function. 225) y = 3 cos x 223) _____ D) 224) Period of f(x) = 2 cos(7πx + 2) A) 7π 222) _____ D) 2 223) Period of f(t) = 3 cos A) 10π B) 10 C) 5 218) _____ D) 219) Period of f(x) = cos 3x A) 3 216) _____ D) 224) _____ 225) _____ A) B) C) D) 226) y = 1.5 sin x 226) _____ A) B) C) D) 227) y = tan x 227) _____ A) B) C) D) 228) y = cos 228) _____ A) B) C) D) 229) y = -cos(πx) 229) _____ A) B) C) D) 230) y = sin 230) _____ A) B) C) D) 231) y = -2 cos 231) _____ A) B) C) D) 232) y = sin(x + π) 232) _____ A) B) C) D) 233) y = tan 233) _____ A) B) C) D) 234) y = 4 sin(x – π) + 4 234) _____ A) B) C) D) Solve the problem. 235) Sales of snow shovels are seasonal. Suppose the sale of snow shovels in Maine is approximated by where t is time in months and t = 0 is October. What are the sales in December? 235) _____ A) 15,000 snow shovels B) 18,660 snow shovels C) 13,900 snow shovels D) 17,071 snow shovels 236) The temperature in Fairbanks is approximated by day x, with x = 1 corresponding to Jan 1 and degree, on day 345. 236) _____ where T(x) is the temperature on corresponding to Dec 31. Estimate the temperature, to the nearest A) -32° B) 338° C) -25° D) -7° 237) A scientist studying ocean tides places an 8 ft high marker in the water at 6 am on a Monday morning. At that time the water is about 5.5 ft high and receding. The scientist observes that the water reaches its lowest level, 0.1 ft, at 9:18 am and then begins to rise. Assume that the water level, in feet, is given by h(t) = 4.9 sin + 5, where t represents the number of hours after midnight. (In other words, the marker was placed in the water when t = 6.) Find the first time interval during which the marker is completely underwater. 237) _____ A) Approximately from 1:18 am to 4:54 am Tuesday B) Approximately from 11:24 pm Monday to 2:00 am Tuesday C) Approximately from 1:42 pm to 5:18 pm Monday D) Approximately from 2:06 pm to 4:24 pm Monday 238) The voltage E in an electrical circuit is given by E = 7.1 cos(60πt), where t is time measured in seconds. Find the period. 238) _____ A) 30π B) 30 C) D) 239) The total sales in dollars of some small businesses fluctuates according to the equation the time in months, with corresponding to January, total sales and give the sales in that month. 239) _____ and where x is Determine the month with the greatest A) September; $4300 B) March; $12,700 C) June; $8500 D) December; $12,700 240) The total sales in dollars of some small businesses fluctuates according to the equation the time in months, with corresponding to January, sales and give the sales in that month. 240) _____ A) September; $3900 C) March; $10,500 , and where x is Determine the month with the least B) December; $7200 D) June; $3300 241) The motion of a spring-mass system is described by the equation where y is the distance in feet from the equilibrium position and t is time in seconds. If the weight is 23 feet from the ceiling in a state of equilibrium, find the time at which the weight first passes the equilibrium position. 241) _____ A) sec B) 1 sec C) 4 sec D) sec 242) The motion of a spring-mass system is described by the equation where y is the distance in feet from the equilibrium position and t is time in seconds. If the weight is 22 feet from the ceiling in a state of equilibrium, find the closest the weight will ever be to the ceiling. 242) _____ A) 22 ft B) 24 ft C) 20 ft D) 2 ft 243) The motion of a spring-mass system is described by the equation where y is the distance in feet from the equilibrium position and t is time in seconds. If the weight is 22 feet from the ceiling in a state of equilibrium, find the distance from the ceiling at time t = 3. 243) _____ A) 34 ft B) 30 ft C) 32 ft D) 28 ft 244) The position of a weight attached to a spring is s(t) = -6 cos(12πt) inches after t seconds. What is the maximum height that the weight reaches above the equilibrium position and when does it first reach the maximum height? 244) _____ A) The maximum height of 12 inches is first reached after 3 seconds. B) The maximum height of 12 inches is first reached after 6 seconds. C) The maximum height of 6 inches is first reached after 6 seconds. D) The maximum height of 6 inches is first reached after 0.08 seconds. 245) The index of refraction for air, Ia, is 1.0003. The index of refraction for water, I w, is 1.3. If and find W to the nearest tenth. 245) _____ A) 22.7° B) 21.7° C) 20.7° D) 23.7° 246) Snell's Law states that find A) . = 6.32 × Use this law to find the requested value. If 246) _____ B) = 6.32 × C) 247) Snell's Law states that find A) B) find = 2.1 × C) =3× Round your answer to the nearest degree. B) find = 48° = 6.08 × and = 31° C) = 32° D) = 49° = 2.67 × 248) _____ = 34° Use this law to find the requested value. If Round your answer to the nearest degree. B) D) Use this law to find the requested value. If 249) Snell's Law states that A) D) 247) _____ = 1.98 × = 35° = 6.85 × Use this law to find the requested value. If 248) Snell's Law states that A) and C) = 46° D) 249) _____ = 51° 250) From a boat on the lake, the angle of elevation to the top of a cliff is 26°29'. If the base of the cliff is 1429 feet from the boat, how high is the cliff (to the nearest foot)? 250) _____ A) 715 ft B) 712 ft C) 725 ft D) 722 ft 251) From a boat on the river below a dam, the angle of elevation to the top of the dam is 21°31'. If the dam is 437 feet above the level of the river, how far is the boat from the base of the dam (to the nearest foot)? A) 1078 ft B) 1088 ft C) 1108 ft 251) _____ D) 1098 ft 252) From a balloon 878 feet high, the angle of depression to the ranger headquarters is 67°34'. How far is the headquarters from a point on the ground directly below the balloon (to the nearest foot)? 252) _____ A) 357 ft B) 352 ft C) 362 ft D) 367 ft 253) When sitting atop a tree and looking down at his pal Joey, the angle of depression of Mack's line of sight is 41°24'. If Joey is known to be standing 20 feet from the base of the tree, how tall is the tree (to the nearest foot)? 253) _____ A) 24 ft B) 18 ft C) 20 ft D) 22 ft 254) The air speed of an airplane is 690 km/hr and its angle of climb is 2.07°. What is its ground speed (to the nearest km/hr)? 254) _____ A) 675 km/hr B) 685 km/hr C) 690 km/hr D) 680 km/hr 255) At an altitude of 3500 ft, the engine on a small plane fails. What angle of glide is needed to reach an airport runway that is 4 miles away by land? (Round your answer to the nearest tenth of a degree.) 255) _____ A) 88.9° B) 89.9° C) 10.4° D) 9.4° 256) The chairlift at a ski resort has a vertical rise of 2400 feet. If the length of the ride is 1.2 miles, what is the average angle of inclination of the lift (to the nearest tenth of a degree)? 256) _____ A) 22.3° B) 19.3° C) 16.3° D) 25.3° 257) A 30-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 your answer to the hundredths place. 257) _____ A) 13.28 ft B) 3.91 ft C) 18.98 ft D) 14.58 ft 258) A contractor needs to know the height of a building to estimate the cost of a job. From a point 89 feet away from the base of the building, the angle of elevation to the top of the building is found to be building. Round your answer to the hundredths place. 258) _____ A) 93.78 ft B) 90.88ft C) 89.35 ft D) 95.11 ft 259) A conservation officer needs to know the width of a river in order to set instruments correctly for a study 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 = 60° (see figure). How wide is the river? Find the height of the 259) _____ A) 52 ft B) 180 ft C) 156 ft D) 78 ft 260) A weight attached to a spring is pulled down 3 inches below the equilibrium position. Assuming that the period of the system is _____ second, determine a trigonometric model that gives the position of the weight at time t seconds. 260) A) y = -3 cos 5πtB) y = -3 cos 10πt C) y = 3 cos 10πt D) y = 3 cos t 261) A weight attached to a spring is pulled down 2 inches below the equilibrium position. Assuming that the frequency of the system is cycles per second, determine a trigonometric model that gives the position of the weight at time t seconds. 261) _____ A) y = -2 cos 10t B) y = 2 cos 10t C) y = 2 cos 5t D) y = -2 cos 5t 262) Tides go up and down in a 14-hour period. The average depth of a certain river is 14 m and ranges from 11 to 17 m. The depth of the river can be approximated by a sine curve. Write an equation that gives the depth x hours after midnight given that high tide occurs at 7:00 am. 262) _____ A) d = 3 sin C) d = 7 sin +1 B) d = 3 sin D) d = 3 sin + 14 + 14 1) D 2) C 3) C 4) D 5) A 6) B 7) C 8) D 9) A 10) C 11) C 12) D 13) D 14) D 15) C 16) A 17) B 18) A 19) B 20) B 21) C 22) D 23) B 24) A 25) D 26) B 27) B 28) D 29) B 30) B 31) A 32) C 33) B 34) A 35) C 36) A 37) A 38) D 39) B 40) D 41) D 42) C 43) A 44) A 45) A 46) C 47) D 48) C 49) C 50) B 51) B 52) A 53) C 54) D 55) A 56) C 57) C 58) B 59) B 60) C 61) B 62) D 63) D 64) A 65) C 66) C 67) C 68) B 69) D 70) A 71) D 72) B 73) B 74) D 75) B 76) B 77) B 78) D 79) A 80) B 81) B 82) A 83) D 84) A 85) A 86) B 87) D 88) B 89) D 90) A 91) D 92) D 93) B 94) A 95) C 96) B 97) B 98) A 99) C 100) D 101) A 102) B 103) B 104) A 105) B 106) B 107) C 108) C 109) D 110) C 111) B 112) C 113) D 114) B 115) B 116) A 117) C 118) C 119) B 120) C 121) C 122) A 123) C 124) B 125) A 126) A 127) A 128) A 129) D 130) B 131) D 132) C 133) D 134) D 135) B 136) A 137) C 138) C 139) C 140) D 141) B 142) D 143) B 144) D 145) B 146) domain: (-∞, ∞), range: (-∞, 0) 147) domain: (-∞, ∞), range: (0, ∞) 148) The graph is shifted 5 units to the right and 5 units down. 149) The graph is reflected over the y-axis and then shifted 3 units down. 150) C 151) C 152) B 153) B 154) C 155) D 156) C 157) B 158) B 159) B 160) C 161) C 162) D 163) D 164) C 165) C 166) A 167) D 168) D 169) B 170) B 171) A 172) A 173) B 174) A 175) B 176) B 177) B 178) B 179) A 180) B 181) C 182) B 183) D 184) C 185) C 186) D 187) C 188) C 189) C 190) B 191) D 192) C 193) A 194) C 195) A 196) A 197) C 198) A 199) D 200) A 201) D 202) D 203) C 204) D 205) C 206) A 207) A 208) C 209) C 210) D 211) C 212) D 213) C 214) B 215) D 216) D 217) A 218) C 219) C 220) B 221) C 222) D 223) B 224) D 225) A 226) D 227) B 228) D 229) D 230) B 231) D 232) C 233) B 234) C 235) A 236) D 237) C 238) D 239) B 240) A 241) D 242) C 243) B 244) D 245) D 246) B 247) C 248) C 249) A 250) B 251) C 252) C 253) B 254) C 255) D 256) A 257) A 258) B 259) C 260) B 261) A 262) D