SECTION 5.1 HOMEWORK ANSWERS
1.
5.
9.
13.
16.
18.
20.
22.
24.
26.
28.
32.
36.
40.
43.
45.
49.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
70.
71.
72.
m = –1
2. m = 2
3. m = -4
4. m = 0
Undefined
6. m = 3/2
7. m = –1
8. m = 1/2
m = 8/5
10. m = –10/9
11. m = –13/6
12. m = 29/12
m=0
14. Undefined
15. m = 2/3; y–intercept is (0,7)
m = –3/5; y–intercept is (0,–9)
17. m = –8/3; y–intercept is (0,7)
m = 3/11; y–intercept is (0,12)
19. m = 0; y–intercept is (0,–4)
m is undefined; no y–intercept
21. m = 3/2; y–intercept is (0,-4)
m = –2/5; y–intercept is (0,9/5)
23. m = –5/2; y–intercept is (0,4)
m = 7/3; y–intercept is (0,–4/3)
25. m = –9/8; y–intercept is (0,9/2)
m = 10/9; y–intercept is (0,–7/9)
27. y = (–2/3)x–4
y = (3/7)x + 9
29. y = 4x + 3/8
30. y = –9x–3.84
31. y = –5
x=0
33. y = 3x + 17
34. y = –5x + 11
35. y = (–3/5)x–46/5
y = (2/7)x + 43/7 37. x = –10
38. y = –11
39. y = –4x–11
y = 6x + 26
41. y = (9/5)x + 22/5 42. y = (–3/4)x–29/4
y= –6x–4
44. y = (21/29)x–1469/290
y = –5.4
46. x = 3.8
47. Parallel
48. Perpendicular
Neither
50. Neither
51. Perpendicular
52. Parallel
Parallel: y = (2/3)x + 19/3 Perpendicular: (–3/2)x+2
Parallel: y = (–3/5)x–6/5 Perpendicular: (5/3)x–8
Parallel: y = –0.7x–9.1
Perpendicular: y = (10/7)x–19/7
Parallel: y = 1.3x + 2.4 Perpendicular: y = (–10/13)x + 85/13
Parallel: f(x) = 3x Perpendicular: f(x) = (–1/3)x + 10
Parallel: g(x) = –5x–28 Perpendicular: g(x) = (1/5)x–36/5
Parallel: y = (–3/2)x–1 Perpendicular: y = (2/3)x–16/3
Parallel: y = (4/5)x + 61/5 Perpendicular: y = (–5/4)x + 4
Parallel: y = 2x–1 Perpendicular: y = (–1/2)x–6
Parallel: y = 4x–13 Perpendicular: y = (–1/4)x + 4
Parallel: y = (3/10)x + 17/2 Perpendicular: y = (–10/3)x–29/3
Parallel: y = (–4/3)x–4 Perpendicular: y = (3/4)x–41/4
Parallel: x = 3 Perpendicular: y = –4
Parallel: y = –5 Perpendicular: x = –2
a. P(x)= –2x + 220
b. 30 pairs of shoes
c. $86
d. Two fewer pairs of shoes are sold if the price is raised $1.
a. W(x)=3x – 630
b. 30 wigs
c. $230
d. Three extra wigs will be produced when the price is raised $1.
a. A(x)=(–1/8)x + 120 b. 35 units
c. $736
d. One less units is rented when the rent is raised $8.
a. P(x) =(–1/5)x + 116 b. 34 passengers
c. $340
d. There is one fewer passenger when the price is raised $5.
a. A(t)=40t + 5200
b. $5,800 in the account
c. The year 2020
d. Each year the money in the account increases $40.
a. V(t)=–110,000t + 2,000,000 b. Value of the warehouse is $350,000
c. Approximately 2018 d. Each year the value of the warehouse depreciates $110,000.
73. a.
c.
74. a.
b.
c.
d.
75. a.
c.
76. a.
c.
77. a.
c.
78. a.
c.
79. a.
c.
80. a.
c.
C(m)=0.15m + 150 b. $228 for 520 miles in one week
400 miles
d. Each mile driven costs $0.15.
A(m) = 0.10(m–200)+200, m> 200, for m<200 A(m) = 200
$232 for 520 miles in one week
You must drive over 600 miles
It costs $0.10 extra for each mile over 200 miles
m(t)=–0.4t + 8.4
b. 4.8 per1,000
Approximately the year 2000
L(t)=–0.02t + 0.49 b. $0.39 a pound
Approximately the year 2004
C(t)=–2t + 22
b. 2 students per computer
1999
M(t)=–3.5t + 34
b. None will be sold
Approximately the year 2000
S(t)=30,000t + 356,000
b. 596,000 millions of dollars
Approximately the year 2000
E(t)=7t+351.2
b. 414.2 quadrillion BTU
Approximately the year 2000
SECTION 5.2 HOMEWORK ANSWERS
1. x = –2, y = 4
2. x = 0.6, y = –2
3. x = 1.5, y = 1
4. x = –3, y = 2
5. x = 8, y = 6
6. x = –12, y = –8
7. x = 3, y = –1
8. x = 3, y = –2
9. x = 6, y = –4
10. x = –3, y = –2
11. x = –5, y = 5
12. x = 8, y = 9
13. x = 3/13, y = 63/13
14. x = –205/23, y = 124/23 15. x = –8, y = –9
16. x = 11/29, y = 28/29 17. x = 34/33, y = –1/11
18. x = 71/124, y = –25/124
19. Same line
20. Same line
21. Parallel lines no solution
22. Parallel lines no solution
23. Same line
24. Parallel lines no solution
25. E(t) = 0.6e0.32189t
L(t) = 17.312ln(t) – 24.862
26. E(t) = 63.24e0.2291t
L(t) = 136.536ln(t) + 5.36
27. E(t) = 410.15e–0.3269t
L(t) = –106.382ln(t) + 251.215
28. E(t) = 284.34e –0.2483t
29.
30.
31.
32.
33.
a.
a.
a.
a.
a.
B(t) = 30e0.2304t
P(t) = 301e0.032t
R(t) = 1562e–0.0446t
P(t) = 36772e–0.0247t
I(t) = 2638e0.0522t
L(t) = –100.319ln(t) + 245.2117
b.
b.
b.
b.
B(t) = 1,349.294ln(t) – 2,806.86
P(t) = 530.255ln(t) – 1018.5
R(t) = –493.26ln(t) + 2135.77
P(t) = –2728.39ln(t) + 36891.18
b. I(t) = 664.62ln(t) + 2355.05
Exponential function
is the best fit.
34. a. S(t)=583.15e0.0514t
Logarithmic function
is the best fit.
35. a. F(t) = 2,101,424e–0.0028665t
Exponential function and
logarithmic function both
fit equally well.
36. a. F(t) = 1,238,803e–0.011415t
Exponential function
is the best fit.
SECTION 5.3 HOMEWORK ANSWERS
1. a. y = 0.00263x + .13036
c. y = 0.0813 + 0.0333ln(x)
e. linear, quadratic, and exponential
2. a. y = –0.00309x + .8459
c. y = 0.8704 – 0.02666ln(x)
e. all seem to fit equally well
3. a. y = 0.1822x + 67.75
c. y = 66.8589 + 2.098ln(x)
e. linear, quadratic and exponential
4. a. y = 1.038x + 9.7796
c. y = 9.5962 + 3.6621ln(x)
e. logarithmic
5. a. y = –3.9276 + 1.4023x
c. y = –23.195 + 14.6919ln(x)
e. logarithmic and quadratic
b. S(t) = 661.27ln(t)–547.64
b. F(t) = –23,315.2ln(t) + 2,109,044.36
b. F(t) = –763,358.9ln(t) + 1,280,986.8
b. y = –3.254x2 + 0.011x + 0.1812
d. y = (0.1326)(1.01656)x
b. y = –0.000284x2 + 0.002668x + 0.8269
d. y = (0.8464)(0.9962)x
b. y = 0.0002822x2 + 0.1678x + 67.8569
d. y = (67.8358)(1.0025)x
b. y = –0.0553x2 + 1.5356x + 8.9502
d. y = (10.1182)(1.0785)x
b. y = –0.04905x2 + 2.4766x – 9.4216
d. y = (2.3782)(1.146)x
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
a. y = –317.1143x + 15271.2952
b. y = –62.6429x2 + 371.9571x + 13559.0571
c. y = 16078.905–1544.7206ln(x)
d. y = ((15398.5456)(0.9766)x
e. quadratic
a. y = –23.082x + 713.1602
b. y = –0.1456x2 – 20.7519x + 707.3348
c. y = 706.7761 – 109.0435ln(x)
d. y = (736.532)(0.9564)x
e. exponential
a. y = 128.4487x + 7480.2359
b. y = 0.6756x2 + 108.2378x + 7594.7317
c. y = 5732.8809 + 1437.5795ln(x)
d. (7620.5594)(1.01379)x
e. linear, quadratic, exponential
a. y = 43.219x – 169.0524
b. y = 1.0919x2 2.8186x + 61.3395
c. y = –262.1561 + 352.0914ln(x)
d. y = (80.693)(1.0914)x
e. quadratic
a. y = 110.0143x – 889.5714
b. y = 5.1314x2 – 95.2429x + 649.8571
c. y = –2914.6734 + 1494.4861ln(x) d. y = (120.6784)(1.1012)x
e. quadratic
a. y = 3.3514x + 25.3019
b. y = 0.2x2 + 1.5514x + 28.7686
c. y = 21.8387 + 13.0517ln(x)
d. y = (27.508)(1.0866)x
e. linear, quadratic and exponential
a. y = 0.8486x + 25.08286
b. y = –0.08036x2 + 1.7325x + 22.8864
c. y = 22.5179 + 4.378ln(x)
d. y = (25.3711)(1.0291)x
e. logarithmic
a. y = 163.0207x + 1111.6568
b. y = 3.8014x2 – 5.7535x + 2164.212
c. y = 996.4759+1373.4747ln(x)
d. (1905.4835)(1.03725)x
e. quadratic and exponential
a. y = –32.09286x + 2031.9286
b. y = –0.4002x2 – 10.0798x + 1781.7798
c. y = 3475.809 – 724.8211ln(x)
d. y = (2527.4019)(0.9695)x
e. quadratic
a. y = 0.1953x + 3.8111
b. y = 0.02057x2 + 0.03071x + 4.058
c. y = 3.8977 + 0.5703ln(x)
d. y = (3.8657)(1.043)x
e. linear and exponential
a. y = 15.7363x – 56.023
b. y = –0.002995x2 + 15.8492x –56.9274
c. y = –529.06508 + 270.5157ln(x)
d. y = (51.4904)(1.0769)x
e. linear and quadratic
a. y = 0.1362x + 0.6529
b. y = 0.0118x2 – 0.1823x + 2.741
c. y = –2.00975 + 1.7733ln(x)
d. y = (1.1902)(1.0556)x
e. quadratic
a. y = 68.1786x + 47.4643
b. y = –0.3869x2 + 78.625x – 21.0179
c. y = –1360.4566 + 899.6972ln(x)
d. y = (363.2995)(1.0742)x
e. all seem to fit equally well
a. y = –0.0376x2 + 3.4715x – 21.8458 b. y = (2.9645)(1.1218)x
c. quadratic function
d. quadratic ≈ 39.8 exponential ≈ 46.8
e. quadratic ≈ 41.4 exponential ≈ 52.5
f. exponential
a. Line function: y = –11.2765x + 815.3221
Quadratic function: y = –16.6789x2 + 1339.7162x – 26187.852
Logarithm function: y = 1504.3764 – 310.1027ln(x)
21.
22.
23.
24.
Exponential function: y = (9813.5194)(0.8911)x
b. no
c. yes
a. y = 10(0.9527)t
b. R(t) = 10e–0.048455t
c. Approximately 14.3 days
d. Phosphorus–32
a. y = 10(0.9772)t
b. R(t) = 10e–0.023064t
c. 30 years
d. Cesium–137
a. y = 500(1.083)t
b. A(t) = 500e0.08t
c. 8%
a. y = 1000(1.1052)t
b. A(t) = 1000e0.10t
c. 10%
SECTION 5.4 HOMEWORK ANSWERS
1.
a.
x y 1st common diff.
2 11
5 20 9
8 29 9
11 38 9
14 47 9
c. y = 3x + 5
e.
2.
a.
b.
d. y = 3x + 5
b.
st
x y
1 Com. Dif
2 9
5 66 57
8 177 111
11 342 165
14 561 219
c. y = 3x2 – 2x + 1
nd
2 Com. Diff.
54
54
54
d.
3.
a.
b.
x
y
Common Ratio
2 12
5 96
8 768
11 6,144
14 49,152
c. y = 3(2)x
8
8
8
8
d. y = 3(2)x
e.
4.
a.
b. y = 3 + 2ln(x)
c. y = 3 + 2 ln(x)
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
20.
21.
22.
23.
24.
25.
26.
d.
a. y = 350t + 5000
b. $17,250
a. y = 83t + 1000
b. $3,075
t
a. y = 9.961215655(0.8871908943) b. Approximately 0.22 grams
a. y = 20.00599018(0.9950114023)t b. Approximately 0.55 grams
a. y = 5,000(1.08)t
b. Approximately $73,926.72
c. 8%
a. y = 1000(1.072)t
b. Approximately $11,397.71
c. 7.2%
y = 2,516.2x + 261,456.4
y = 24,200.3x + 153,441.6
y = 0.2928571429x2 + 2.598571429x + 77.44571429
y = 544.642857x2 + 4,436.928571x + 220,345.0857
y = 932.3885107 + 188.4429424 ln(x)
y = 608.5x + 10,958.9
y = 9.795424857/(1 + 1.067453932e–0.0238215966x)
y = 36,114.55826/(1+0.3055708166e–0.8395598572x)
y = 235.5714286x2  6,111.085714x +505,572.5429
y = 1,821.428571x2 + 111,098.6286x + 1,233,055.6
y = 432.3700173x + 18,409.77383
y = 57.5x2 + 2696.3x + 80,895.6
y = 0.0966397644x2 + 85.35755523x – 690.0824742
y = 36.14285714x2 + 8.142857143x + 6,890.4
y = 23,973x + 299,537.2
y = 10,814x + 293,124.2
27.
28.
29.
30.
y = 19.92142857x2 + 237.6642857x + 4,972.802857
y = 4.957142857x2 + 19.89142857x + 804.5142857
y = –25.38938181 + 14.20221005 ln(x)
y = –5.453660777 + 2.935692901 ln(x)
CHAPTER FIVE REVIEW HOMEWORK ANSWERS
1.
5
4
5.
Slope =
7.
9.
11.
13.
15.
16.
17.
18.
19.
20.
21.
24.
27.
29.
30.
31.
2.
4
9
3.
Zero
4. Undefined
3
2
5
; y–intercept (0, 7)
6. Slope =
; y–intercept (0, )
5
3
3
Undefined slope; No y–intercept
8. Slope = 0; y–intercept (0, –3)
3
3
19
y  x 5
x
10. y 
5
5
5
3
x
12. y = –2
8
7
41
2
11
y x
x
14. y 
4
4
5
5
3
11
5
7
x
Parallel: y 
Perpendicular: y  x 
5
5
3
3
2
3
1
x
Parallel: y  x  7
Perpendicular: y 
3
2
2
1
x  110
a. g ( x ) 
b. 65
c. $116
2
d. For every increase of $2 per glove one less glove will be sold.
a. E(t) = –120,000t + 1,200,000
b. $480,000
c. 3 years
a. M(t) = 0.07t + 4.71
b. 506,000
c. 2010
a. H(t) = –0.2t + 84.8
b. 84%
c. 2000
131
 29
x = 6; y = 4
22. x = 2; y = 0
23. x =
; y=
31
31
689
 506
 22
7
x = –2; y = 1
25. x =
; y=
26. x =
; y=
9
3
163
163
No solution Parallel lines
28. Same line
E(t) = 10.001e0.231t
L(t) = –40 + 54.614 ln (t)
a. B(t) = 6,249,778e–0.022314t
a. F(t) = 384.3 e0.0494938801t
c.
Logarithmic
b.
b.
B(t) = 11,212,567–4481420.118 ln(t)
F(t) = 199.4 ln(t) + 171.3
32.
34.
35.
y = 58.65x + 2675.6
33. y = –77.1x + 2691.9
y = 17.94696133x2 + 330.2071823x + 5877.841436
y = 78.45566727 – 17.08148562 ln(x)