1. Exponential Function2. Exponential Function3. Exponential Function

SECTION 4.1 HOMEWORK ANSWERS

1. Exponential function2. Exponential function3. Exponential function

4. Exponential function5. Linear function6. Linear function

7. Neither8. Neither9. Exponential function

10. Exponential function11. Linear function12. Linear function

13. Linear function14. Exponential function15. Exponential function

16. Linear function17. Linear function18.Exponential function

19. Exponential function20. Linear or Exponential function

21.a) 1.08,1.08, 1.08b.) 1.08c.) A(t) = 5000(1.08)t
d.) $23,304.79e.) Growth

22. a.)

b.) 2c.) B(t) = (4)2td.) 4096 bacteriae.) Growth

23.a) 1.1, 1.1, 1.1b.) 1.1c.) F(t) = 100,000(1.1)t
d.) 161,051 fishe.) Growth

24. a) 1.02, 1.02, 1.02b.) 1.02c.) P(t) = 500,000(1.02)t
d.) 585,830 peoplee.) Growth

25. a) 0.96, 0.96, 0.96b.) 0.96c.) P(t) = 1,000,000(0.96)t
d.) 721,390 peoplee.) Decay

26. a) 0.95, 0.95, 0.95b.) 0.95c.) F(t) = 200,000(0.95)t
d.) 147,018 treese.) Decay

27. a) 0.8, 0.8, 0.8b.) 0.8c.) S(t) = 150(0.8)t
d.) 16,106 whalese.) Decay

28. a) 0.82, 0.82, 0.82b.) 0.82c.) R(t) = 20(0.82)t
d.) 2.7490 gramse.) Decay

29. a.) f(x) = 2xb.) Growth30. a.) f(x) =b.) Growth

31. a.) f(x) = (0.5)xb.) Decay32. a.) f(x) = (0.3)xb.) Decay

33.a.) f(x) = 2(3)xb.) Growth34. a.) f(x) =b.) Growth

SECTION 4.2 ANSWERS FOR HOMEWORK

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.a.) Decayb.) All real numbersc.) (0, )d.) (0, 20)

16.a.) Decayb.) All real numbersc.) (0, )d.) (0, 15)

17.a.) Growthb.) All real numbersc.) (0, )d.) (0, 50)

18.a.) Growthb.) All real numbersc.) (0, )d.) (0, 10)

19.a.) Growthb.) All real numbersc.) (0, )d.) (0, 5000)

20.a.) Growthb.) All real numbersc.) (0, )d.) (0, 10000)

21.a.) Decayb.) All real numbersc.) (0, )d.) (0, 1)

22.a.) Decayb.) All real numbersc.) (0, )d.) (0, 1)

23.a.) Decayb.) All real numbersc.) (5, )d.) (0, 6)

24.a.) Decayb.) All real numbersc.) (2, )d.) (0, 1)

25.a.) Growthb.) All real numbersc.) (3, )d.) (0, 2)

26.a.) Growthb.) All real numbersc.) (2, )d.) (0, 3)

27.a.) Growthb.) All real numbersc.) (10, )d.) (0, 20)

28.a.) Growthb.) All real numbersc.) (10, )d.) (0, 10)

29. 430. 231. 632. 5

33. –234. –335. –436. –4

37. 038. 039. 140. 1

41. No solution42. No solution

43.a.) –1b.) 0c.) 1d.) 2e.) 3

44.a.) –1b.) 0c.) 1d.) 2e.) 3

45.a.) –1b.) 0c.) 1d.) 2e.) 3

46.a.) –1b.) 0c.) 1d.) 2e.) 3

47.a.) –1b.) 0c.) 1d.) 2e.) 3

48.a.) –1b.) 0c.) 1d.) 2e.) 3

49.a.) –1b.) 0c.) 1d.) 2e.) 3

50.a.) –1b.) 0c.) 1d.) 2e.) 3

51. 52.

53. 54.

55. 56.

57. 58.

59. 2.2660. 2.2661. 6.6462. 3.86

63. 3.0764. 2.19

65. y = 10(3)x has y–intercept at (0,10) and y = 3x has a y–intercept at (0,1).

66. y = 5(2)x has a y–intercept at (0,5) and y = 2x has a y–intercept at (0,1).

67. y = 8(1/2)x has a y–intercept at (0,8) and y = (1/2)x has a y–intercept at (0,1).

68. y = 3(5)x has a y–intercept at (0,3) and y = 5x has a y–intercept at (0,1).

69. a.) y = 2x + 5 has a y–intercept at (0,6) and y = 2x has a y–intercept at (0,1).

b.) y = 2x + 5 has a range of (5, ) any y = 2x has a range of (0, ).

70. a.) y = 3x – 4 has a y–intercept at (0,–3) and y = 3x has a y–intercept at (0,1).

b.) y = 3x – 4 has a range of (–4, ) and y = 3x has a range of (0, ).

71. a.) y = (1/2)x +3 has a y–intercept at (0, 4) and y = (1/2)x has a y–intercept at (0,1).

b.) y = (1/2)x +3 has a range of (3, ) and y = (1/2)x has a range of (0, ).

72. a.) y = 4x + 2 has a y–intercept at (0, 3) and y = 4x has a y–intercept at (0,1).

b.) y = 4x + 2 has a range of (2, ) and y = 4x has a range of (0, ).

73. a.) y = 3(2)x+2 has a y–intercept at (0,5) and y = 2x has a y–intercept at (0,1).

b.) y = 3(2)x+2 has a range of (2, ) and y = 2x has a range of (0, ).

SECTION 4.3 ANSWERS FOR HOMEWORK

1. 3y =x2. a3 = w3. 5x = 2

4. 3–2 = x5. 2a = x+y6. ax+2 = 3

7. log3 m = x8. logy r = 39. loga 5 = 3x–1

10. log3 6 = 2x+311. loga (x+y) = 512. log3 (2x–3) = b

13. log3 3 + log3 x14. log3 a + log3 r15. log2 x – log2 3

16. log2 5 – log2 b17. log x + log y – log 5 – log z

18. log 3 + log a – log 2 – log b19. 2log5 x + log5 y20. 3log5 x + (1/2)log5 y

21. 3ln a – 2 ln x – ln y22. 3ln a + 2 ln b – ln x

23. log4 3 + log4 y + (1/3)log4 x – log4 a – 2log4 b

24. 2log4 x +3log4 y – log4 3 – (1/4)log4 a

25. (2/3)ln x + (1/3)ln y – (1/3)ln a

26. (1/4)log 3 + (1/2)log a – (1/4)log b – (1/2)log c

27. log2 3x28. log2 5a29. log5 (r/4)

30. log5 (7/x)31. log(x(2x–1))32. log((2x–1)(3x+2))

33. log 34. 35.

36. 37. 38.

39. 40. 41. = ln 1 = 0

42. = log 1 = 0

43. a.) 1.5563b.) 1.5563c.) 1.5563d.) 1.5563

Property loga bc = loga b + loga c

44. a.) 4.6052b.) 4.6052c.) 4.6052d.) 4.6052

Property: loga bc = loga b + loga c

45. a.) 1.6094b.) 1.6094c.) 1.6094d.) 1.6094

Property: loga (b/c) = loga b – loga c

46. a.) 0.9031b.) 0.9031c.) 0.9031d.) 0.9031

Property: loga (b/c) = loga b – loga c

47. a.) 2.0969b.) 2.0969 Property: loga bn = nloga b

48. a.) 5.4931b.) 5.4931Property: loga bn = nloga b

49. a.) –3.2189b.) –3.2189Property: loga bn = nloga b

50. a.) –0.9031b.) –0.9031Property: loga bn = nloga b

51. ln 15 ≈ 2.7081ln 3 + ln 5 ≈ 2.7081

52. log 33 ≈ 1.5185log 3 + log 11 ≈ 1.5185

53. log 3 ≈ 0.4771log a – log b, where (a/b) =3 i.e. log 24 – log 8 ≈ 0.4771

54. ln 7 ≈ 1.9459ln a – ln b, where (a/b) = 7 i. e. ln 14 – ln 2 ≈ 1.9459

55. 2 log 5 + 2log 8 – 2log 10 ≈ 1.2041 ≈ 1.2041

56. 3log 2 + 2log 3 – 3 log 6 ≈ –0.4771 ≈ –0.4771

57. 2.5335 check 52.5335 ≈ 58.998458. 3.4713 check 43.4713 ≈ 123.0072

59. 2.6049 check 72.6049 ≈ 158.999560. 3.0423 check 63.0423 ≈ 233.0073

61. 4.5236 check (1/2)4.5236 ≈ 0.0435 ((1/23) ≈ 0.0435)

62. –1.6826 check (1/5)–1.6826 ≈ 14.9999

63. –2.2619 check 3–2.2619 ≈ 0.0833 ((1/12) ≈ 0.0833)

64. –1.1469 check 5–1.1469 ≈ 0.1579 ((3/19) ≈ 0.1579)

65. No answer66. No answer

67. No answer68. No answer

69. Domain: (0, ) Range: (–,)70. Domain: (0 , ) Range: (–,)

71. Domain: (0, ) Range: (–,)72. Domain: (0, ) Range: (–,)

73. Domain: (0, ) Range: (–,)74. Domain: (0, ) Range: (–,)

75. Domain: (0, ) Range: (–,)76. Domain: (0, ) Range: (–,)

77. (–, 0)78. (0, )79. (–(1/3), )

80. ((8/5), )81. (–,–4) or (4, )82. (–,–2.5) or (2.5, )

SECTION 4.4 ANSWERS FOR HOMEWORK

1. x = 1.52. x = 13. x = 5

4. x = 15. x = 3.56. x = 4/3

7. x = 8. x =

9. x = 10. x = 11. x =

12. x = 13. x = 14. x =

15. x = 16. x = 17. x =

18. x = 19. x = 20. x =

21. x = 22. x = 23. x =

24. x = 25. x =

26. x =

27. x = 528. x = 23/529. x = 9

30. x = 17/231. No solution32. No solution

33. x = 234. x = 5/335. x =

36. x = 37. x = 38. x =

39. No solution40. No solution41. No solution

42. No solution43. x = 1044. x = 12

45. x = 1446. x = 3

47. x = 248. x = 13/249. x = 13/5

50. x = 97/1251. x = 11/552. x = 7/3

53. x = 454. x = 455. x =

56. x = 57. No solution58. No solution

59. No solution60. No solution

61. a. 7b. 3.55c. 3.98 x 107d. 6.3 x 104

62. a. 4.5b. 6.5c. 103I0d. 105I0e. 100 times

63. a. Approx. 56.2 minutesb. Approx. 15.8 hoursc. Approx. 90.50

64. a. Approx. 16,438 fishb. Approx. 20 months

65. a. Approx. 338 snailsb. Approx. 15.4 months

66. a. Approx. 37 bacteriab. Approx. 19.1 minutes

67. a. Approx. $49.530.32b. Approx. 20.1 years

68. a. Approx. $120, 183.03b. Approx. 18 years

69. a. Approx. 6.3 gramsb. Approx. 34.8 hours

70. a. Approx. 31.5 gramsb. Approx. 99.7 years

SECTION 4.5 ANSWERS FOR HOMEWORK

1.

Yearly

Monthly

Quarterly

Weekly

Yearly

Monthly

Yearly

Monthly

2.

3. $25,113.194. $1,068,240.675. $192,106.56

6. $9,001.927. $3,109.438. $4,120.07

9. a. Approx. 57.8 years b. Approx. 46.2 years c. Approx. 57.6 years d. Approx. 46 years

10. a. Approx. 14.6 years b. Approx. 11.33 years c. Approx. 14.59 years d. Approx. 11.31 years

11. a. Approx. 9 years b. Approx. 8 years c. Approx. 7.3 years d. Approx. 6.1 years

12. a. Approx. 8.2 years b. Approx. 7.3 years c. Approx. 6.6 years d. Approx. 5.6 years

13. a. Approx. 15.7 yearsb. Approx. 12.2 yearsc. Approx. 10 years

14. a. Approx. 10.7 yearsb. Approx. 8.2 yearsc. Approx. 6.6 years

15. $50,664.1116. $103,078.4217. Approx. 6.3 years

18. Approx. 6.2 years19. Approx. 6.7 years20. Approx. 10.7 years

21. Approx. $3,966.8722. Approx. $17,949.93823. Approx. 11.75%

24. Approx. 9.3%25. $1,121,4626. $1,310.25

SECTION 4.6 ANSWERS FOR HOMEWORK

1. $104,520.912. $116,885.003. $898,255.094. $275,711.14

5. a.) $118,825.28 b.) $91,825.28 6. a.) $584,418.74b.) $486,918.74

7. a.) Approx. $104.74 b.) $25,137.60 of own money and $32,862.40 interest

8. a.) Approx. $87.95 b.) $21,108.00 of own money and $36,892.00 interest

9. Approx. $57.70own money $18,002.40 and $5,997.60 interest 10. Approx. $39.09

11. Approx. $78.6412. Approx. $60.0813. Approx. $197.64

14. a.) Approx. $171.18 b.) $61,339.20 total for two week and $61,624.80 total for monthly

15. Approx. 25 years16. Approx. 20 years

17. Approx. 9%18. Approx. 8.5%

19. a.) Monthly payments of approx. $1,100.65 amount of total interest paid is $246,234

b.) Monthly payments of approx. $1,048.82 amount of total interest paid is $227,575.20

c.) Monthly payments of approx. $1,348.24 amount of total interest paid is $92,683.20

d.) Monthly payments of approx. $1,306.66 amount of total interest paid is $85,198.80

20.a.) Monthly payments of approx. $820.17 amount of total interest paid is $2,526.12

b.) Monthly payments of approx. $640.30 amount of total interest paid is $3,734.40

c.) Monthly payments of approx. $547.46 amount of total interest paid is $5,847.60

d.) Monthly payments of approx. $480.02 amount of total interest paid is $7,561.44

21. Best deal is 8% with $3,000 back as a down payment

22. Best deal is 2.5% a month

23. a.) You can buy a home for $147,186.17 b.) You can buy a home for $158,316.85

24. a.) You can buy a car for $21,209.76 b.) You can buy a car for $24,038.35

25.a.) You can buy furniture worth $4,682.68

b.) You can buy furniture worth $5,891.89

26.a.) You can buy a home worth $148,344.03

b.) You can buy a home worth $142,122.01

27. Approx. 7.9% interest rate28. Approx. 16.5% interest rate

29.Approx. 48 months30. Approx. 18 months

31. a. Approximately 6.4 years or 77 months

b. Approximately $16,940 total payments

c. Approximately $6,940 interest paid

32.a. Approximately 7.6 years or 91 months

b. Approximately $16,380 total payments

c. Approximately $7,980 interest paid

33. a.) b. Looks Linear

34. a.) b. looks Exponential

35. a.) b. Looks Linear

36.a.) R(t) = 50,000 b. Looks exponential

37.R(t) = Looks Linear

a. Approximate payments for a four year loan $488.26

b. Approximate payments for a five year loan $405.53

c. Approximate payments for a ten year loan $242.66

38. R(L) = Looks Linear

a. Approximate payments for a $7,000 loan $90.58.

b. Approximate payments for a $8,000 loan $103.52.

c. Approximate payments for a $4,000 loan $51.76.

SECTION 4.7 ANSWERS FOR HOMEWORK

1. a. R = 10e0.05776tb. Approx. 1.4866 grams

2.a. R = 20e0.13863tb. Approx. 0.4123 grams

3.a. R = 15e0.000428tb. Approx. 10.2047 grams

4.a. R = 300.0000000005415tb. Approx. 29.9984 grams

5.a. R = 10e0.0231tb. Approx. 30 years

c. Approx. 3.1506 gramsd. Cesium–137

6.a. R = 40e0.0357tb. Approx. 19.4 years

c. Approx. 13.7066 gramsd. Lead–210

7.a. R = 50e0.165tb. Approx. 4.2 days

c. Approx. 0.3542 gramsd. Thallium–206

8.a. R = 100e0.00796tb. Approx. 87 days

c. Approx. 62.027 gramsd. None

9. Approx. 2,820,903,237 years old 10. Approx. 1,839,549,228 years old

11. Approx. 7,575 years old 12. Approx. 19,034 years old

13.a. Approx. 28 yearsb. Approx. 280 years

14.a. Approx. 24,407 yearsb. Approx. 244,070 years

15.a. Approx. 6 hoursb. Approx. 60 hours

16.a. Approx. 8 daysb. Approx. 80 days

17. a. A =20e0.32189tb. Growthc. 312,523 ants

18.a. R = 3e0.74893tb. Growthc. 23,999 rabbits

19.a. P = 12500e0.03646tb. Growthc. 37,320 peopled. 19 years

20.a. P = 280000e0.04823tb. Decayc. Year 2005

21.a. P = 50000.07438tb. Decayc. Approx. 30 days

22.a. F = 10e.29957tb. Growthc. Approx. 15 days

23.a. Approx. 4.5 minutesb. Approx. 13 minutes

24.a. Approx. 59.9ob. Approx. 10 minutes

25.a. Approx. 112.6ob. Approx. 128 minutes

c. Approx. 156 minutes

26.a. Approx. 33.7ob. Approx. 81 minutes

27.a. y = 3,321,000(1.006153)tb. y = 3,321,000e0.006135t

c. y= 3,321,000(1.006153)83,488,037 votes y = 3,321,000 e(0.006135)(8)3,488,061 votes

28.a. y = 8,334,000(0.99573)tb. y = 8,334,000e0.0042779t

c. y = 8,334,000(0.99573)88,053,529 votes y = 8,334,000 e–0.0042779(8)8,053,609

29. Number 27 is an increasing function and number 28 is a decreasing function.

30.a. k = 0.0563b. Approx. 19.98 gramsc. 19.98e0.0563t

d. Approx. 12.3 dayse. Hydrogen–3

31.a. k = 0.05776b. Approx. 50 gramsc. 50e0.05776t

d. Approx. 12 dayse. Barium–131

32.a. k = 0.04847b. Approx. 10 gramsc. 10e0.04847t

d. Approx. 14.3 dayse. Phosphorus–32

33.a. k = 0.1318b. Approx. 30 gramsc. 30e0.1318t

d. Approx. 5.26 yearse. Cobalt60

SECTION 4.8 ANSWERS FOR HOMEWORK

1. Approx. 20.6 decibels2. Approx. 34 decibels3. Approx. 89.5 decibels

4. Approx. 69.8 decibels5. 1,000,000 I06. Approx. 2,500,345 I0

7. Approx. 1.088930093x1014I08. 1,199,499,303 I09. 4

10. 511. 612. 7

13. 6.514. 3.215. 4.3

16. 6.317. 10,000 I018. 100,000 I0

19. 5011.87 I020. 501,187.23 I021. 19.952.62 I0

22. 31,622.78 I023. 7,943,282.35 I024. 158,489.32 I0

25. pH3.826. pH6.227. pH7.8

28. pH2.929. H+ = 0.000000130. H+ = 0.0001

31. H+ = 0.0000000000132. H+ = 0.00001

33. a. Approx. 79.8%b. Approx. 74 inches tall

34. a. Approx. 75.6%b. Approx. 75.4 inches tall

35. a. Approx. 14 years oldb. Approx. 78.8 inches tall

36. a. Approx. 4 years oldb. Approx. 71.3 inches tall

37. Approx. 8.7 years38. Approx. 11.6 years

39. Approx. 7.4 years40. Approx. 9.2 years

41. Approx. 5%42. Approx. 9%

43. Approx. 0.721944. Approx. 0.913

45. 146. 1

47. Approx. 33 or 300

ANSWERS FOR CHAPTER FOUR REVIEW HOMEWORK

1. Linear2. Exponential3. Exponential4. Linear

5. a. 21,600/20,000 = 1.0823,328/21,600 = 1.0825,194.15/23,328 = 1.08

b. 1.08c. A(t) = 20,000(1.08)td. $93,219.14e. Growth

6. a. 7,800,000/8,000,000 = 0.9757,605,000/7,800,000 = 0.975

7,414,875/7,605,000 = 0.975

b. 0.975c. P(t) = 8,000,000(0.975)td. 6,872,546e. Decay

7. a. Decayb. All real numbersc. (0, )d. (0, 30)

8. a. Growthb. All real numbersc. (0,)d. (0,10)

9. a. Growthb. All real numbersc. (10,)d. (0,11)

10.a. Decayb. All real numbersc. (9, )d. (0,10)

11. 212. 513. 114. 6

15. 016. 217. 318. 3

19. Approx. 1.9520. Approx. 4.0421. Approx. 3.1022. Approx. 6.39

23. ax = 524. 3b = y+325. log5y=x26. loga9=x+3

27. log33 + 3log3x + 2log3y28. (1/2)logx  2logc

29. log53 + 4log5x  3log5a30. ln5 + 5lnx + (1/3)lny  lna  4lnb

31. log3ab532.

33. 34.

35. 2log3 + (1/2)log4  3log5 0.841636. 3ln5 + 4ln2  2ln10 2.9957

37. Approx. 2.275738. Approx. 2.397839. Approx. 3.6309

40. Approx. 7.069141. (0, )42. (, 0)

43. (3/2, )44. (, 2) or (2, )45. x = 2

46. 5/347. Approx. 0.47548. 0.496

49. 50.

51. 52.

53. x = 554. No solution55. x = 14/3

56. x = 457. x = 558. x = 3

59. x = 11/560. x = 2

61. a. Approx. 0.1564 gramsb. 10 gramsc. Approx. 11.6 days

62. a. k0.000462b. Approx. 1,947 days

63. Approx. $317,312.4764. Approx. $100,000.00

65. Approx. 7.3 years66. Approx. $351,434.38

67. Approx. $18,925.2068. Approx. 7.3 years

69. Approx. $1,268.3170. Approx. $21,459.28

71. Approx. $567,170.1472. Approx. $62.90 a month

73. a. R(t) = 5e0.08664tb. Approx. 9 days

74. a. R(t) = 10e0.00446tb. Approx. 205.4 years

75. a. P = 4,500e0.00656tb. Growthc. Approx. the year 2012

76. a. G = 1,000,000e0.227065tb. Decayc. Approx. 4.6 minutes

77. a. Approx. 51.76 decibelsb. 10,000,000,000 Io

78. a. Approx. 86.4%b. Approx. 76.8 inches tall

ANSWERS FOR CHAPTER 4 EXAM

1. a. 125,829/123,000 = 1.023128,723/125,829 = 1.023

b. P = 123,000e0.004548tc. Approx. 130,491 peopled. The year 2010

2. a. Growthb. All real numbersc. (0, 25)

3. 54. Approx. 2.7175. log3 + 3logx  2loga  (1/3)logb

6. 7. ((2/3), )8. x = 1

9. 10. 11. x = 14

12. x = 5

13. x = 28/314. x = 415. Approx. $29,772.78

16. Approx. 6.5%17. Approx. $244.84

18. a. Approx. $1,255.76 a monthb. Approx. $1,642.22 a month c. Approx. $156,474.00

19. a. Approx. 13.6079 gramsb. Approx. 2,141.5 years

20. a. P(t) = 24,000e0.01122tb. Approx. 37,594 people c. The year 1998

21. a. pH3.3b. pH5.3 (It is safest to leave out the oranges.)

22. a. H+0.0063b. H+0.000005 c. H+0.0000004