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
Number of Bacteria / 4 / 8 / 16 / 32 / 64 / 128 / 256
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
x / 1 / 0 / 1 / 2 / 3f(x) / 1/2 / 1 / 2 / 4 / 8
1.
x / 1 / 0 / 1 / 2 / 3f(x) / 1/3 / 1 / 3 / 9 / 27
2.
x / 1 / 0 / 1 / 2 / 3f(x) / 4 / 1 / 1/4 / 1/16 / 1/64
3.
4.
x / 1 / 0 / 1 / 2 / 3f(x) / 2 / 1 / 0.5 / 0.25 / 0.125
5.
x / 1 / 0 / 1 / 2 / 3f(x) / 4 / 1 / 1/4 / 1/16 / 1/64
x / 1 / 0 / 1 / 2 / 3
f(x) / 2 / 1 / 1/2 / 1/4 / 1/8
6.
x / 1 / 0 / 1 / 2 / 3f(x) / 7/2 / 4 / 5 / 7 / 11
7.
x / 1 / 0 / 1 / 2 / 3f(x) / 5/3 / 1 / 1 / 7 / 25
8.
x / 1 / 0 / 1 / 2 / 3f(x) / 2 / 0 / 2/3 / 8/9 / 26/27
9.
x / 1 / 0 / 1 / 2 / 3f(x) / 4 / 3 / 2.5 / 2.25 / 2.125
10.
x / 1 / 0 / 1 / 2 / 3f(x) / 3/2 / 3 / 6 / 12 / 24
11.
x / 1 / 0 / 1 / 2 / 3f(x) / 1 / 2 / 4 / 8 / 16
12.
x / 1 / 0 / 1 / 2 / 3f(x) / 1 / 2 / 4 / 8 / 16
13.
x / 1 / 0 / 1 / 2 / 3f(x) / 4 / 2 / 1 / 1/2 / 1/4
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 107d. 6.3 x 104
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.
InitialInvestment / Compounded / Annual
Percentage
Rate / Doubling
time / Amount
after 10
years / Amount
after 20
years / Amount
after 40
years
$10,000 /
Yearly
/ 8% / 9 years / $21,589.25 / $46,609.57 / $217,245.22$30,000 /
Monthly
/ 9.5% / 7.3years / $77,281.66 / $199,081.84 / $1,321,119.33$11,172.92 /
Quarterly
/ 10% / 7 years / $30,000.00 / $80,551.92 / $580,744.04$11,168.57 /
Weekly
/ 7.5% / 9.25years / $23,613.09 / $50,000.00 / $223,842.39$12,000.00 /
Yearly
/ 8.5% / 8.5 years / $27,131.80 / $61.344.55 / $313,596.19$6,000.00 /
Monthly
/ 12% / 5.8 years / $19,802.32 / $65,355.32 / $711,886.35$10,000.00 /
Yearly
/ 10.5% / 6.9 years / $27,200.00 / $73,662.35 / $542,614.16$5,000.00 /
Monthly
/ 11% / 6.3 years / $15,000.00 / $44,675.08 / $399,172.502.
InitialInvestment / Annual
Percentage
Rate / Doubling
time / Amount
after 10
years / Amount
after 20
years / Amount
after 40 years
$40,000.00 / 9% / 7.7 years / $98,384.12 / $241,985.90 / $1,463,929.38
$25,000.00 / 7.5% / 9.2 years / $52,925.00 / $112,042,23 / $502,138.42
$5,044.93 / 8% / 8.7 years / $11,227.70 / $24,987.70 / $123,764.90
$10,000.01 / 9.5% / 7.3 years / $25,857.10 / $66,858.94 / $447,011.85
$80,000.00 / 7% / 9.9 years / $161,100.22 / $324,416.00 / $1,315,571.74
$10,000.00 / 10.5% / 6.6 years / $28,576.51 / $81,661.70 / $666,863.31
$20,000.00 / 5.5% / 12.6 years / $34,665.06 / $60,000.00 / $180,500.27
$5,000.00 / 8% / 8.7 years / $11,127.70 / $25,000.00 / $122,662.65
$4065.70 / 9% / 7.7 years / $10,000.00 / $24,596.00 / $148,797.44
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 = 10e0.05776tb. Approx. 1.4866 grams
2.a. R = 20e0.13863tb. Approx. 0.4123 grams
3.a. R = 15e0.000428tb. Approx. 10.2047 grams
4.a. R = 300.0000000005415tb. Approx. 29.9984 grams
5.a. R = 10e0.0231tb. Approx. 30 years
c. Approx. 3.1506 gramsd. Cesium–137
6.a. R = 40e0.0357tb. Approx. 19.4 years
c. Approx. 13.7066 gramsd. Lead–210
7.a. R = 50e0.165tb. Approx. 4.2 days
c. Approx. 0.3542 gramsd. Thallium–206
8.a. R = 100e0.00796tb. 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 = 280000e0.04823tb. Decayc. Year 2005
21.a. P = 50000.07438tb. 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)83,488,037 votes y = 3,321,000 e(0.006135)(8)3,488,061 votes
28.a. y = 8,334,000(0.99573)tb. y = 8,334,000e0.0042779t
c. y = 8,334,000(0.99573)88,053,529 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. 19.98e0.0563t
d. Approx. 12.3 dayse. Hydrogen–3
31.a. k = 0.05776b. Approx. 50 gramsc. 50e0.05776t
d. Approx. 12 dayse. Barium–131
32.a. k = 0.04847b. Approx. 10 gramsc. 10e0.04847t
d. Approx. 14.3 dayse. Phosphorus–32
33.a. k = 0.1318b. Approx. 30 gramsc. 30e0.1318t
d. Approx. 5.26 yearse. Cobalt60
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. k0.000462b. 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) = 5e0.08664tb. Approx. 9 days
74. a. R(t) = 10e0.00446tb. Approx. 205.4 years
75. a. P = 4,500e0.00656tb. Growthc. Approx. the year 2012
76. a. G = 1,000,000e0.227065tb. 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