A-40 Answers
53. AB
54. AB
10. (A) 8 ways:
H
(H, H, T)
T
H(H, H, H )
9. (A) 12 combined outcomes:
1
2
8
8
8
8
5
36. 3#5#2=30 37. 52
5
=380,204,032 38. 625=916,132,832
39. 10 #9#8#7#
6
=30,240; 10 #10 #10 #10 #10 =100,000; 10 #9#9#9#9
6
5
5
3
5
5
8
5
6
44. A¨B⊂C 45. z 46. y 47. x and z 48. w 49. 14 50. 6
4
3
3
2
4
3
3
2
4
3
3
HA
P
Start MA
P
2
58. (A) 490 (B) 310 (C) 240
59. 1,570 60. 1,550 61. (A) 102,000
62. (A) 367,000 (B) 220,000 (C) 1,435,000 (D) 1,790,000
63. (A) 12 classifications:
U
NA
O
64. (A) 8 ways:
B
B
(B, B, B)
Exercises 7.4
34. Permutation 35. Neither 36. Neither 37.
1
0
P
3
=10 #9#8=720
6
6
3
6
5
8
3
3
3
4
5
5
5
6
8
74. (A) 28C12 =30,421,755 (B)
14C5#8C4#6C3=2,802,800
75. (A)
6
C
3
#
5
C2=200 (B)
6
C4#
5
C1=75 (C)
6
C
5
=
6
(D)
11C
5
=4
6
2
Chapter 7 Review Exercises
less than 3
2
, then 3
4
is less than 4
3
; false (7.1) 5. If 3
4
is less than 4
3
, then 2
3
is less than 3
2
; true (7.1) 6. If 3
4
is not less than 4
3
, then 2
3
is not less than
11. Conditional; true (7.1) 12. Disjunction; false (7.1) 13. Conjunction;
positive: If the square matrix A has an inverse, then the square matrix A does not
have a row of zeros. (7.1) 16. Converse: If the square matrix A has an inverse,
3H
T
T
5H
T
24. 360,360 (7.4) 25. 3,003 (7.4)
26. 56 (7.4) 27. 6720 (7.4)
28. 9,295 (7.4)
29. 6#
5
#4#3#2#1=720 (7.3)
32. pqp¡
1
qSp
2
TT T
Contingency (7.1)
TF F
A-42 Answers
36. pq
TT F
TF F
FT T
FF F
37. Infinite (7.2) 38. Finite (7.2) 39. Infinite (7.2) 40. Infinite (7.2)
43. AB
6
3
(7.2) 44. 5 children, 15 grandchil-
(7.3) 46. (A)
6
P
3
=120
5
61. pq
TT T
TF T
FT F
FF F
62. pq
p
¡
q
¬
p
S
q
TF T T
(7.1)
63. pq
Chapter 8
Exercises 8.1
1. E 2. F 3. F 4. E 5. F 6. E 7.
3
8.
5
9.
1
5
10.
1
5
11. 0
2
1
1
1
9
1
1
4
1
4
8
8
365
6
8
3
1
3
1
3
6
1
6
6
1
8
50
1
3
2
3
3
3
3
5
5
6
5
3
3
3
5
4
60
3
ANSWERS
and, in addition, 365! produces an overflow error on many calculators, while
365
P
n does not produce an overflow error for many values of n.
12!
77. (A) 11
+7
=
18
=.36 (B)
6
+
5
=11
≈.306 (C) Answer
A-44 Answers
Copyright © Pearson Education, Inc.
2
15. .375 16. .625 17. .10 18. .50 19. .15 20. .10 21. .75
1
2
1
2
1
3
pi.0002 .0006 .001 .004 .9942
40. Probability distribution:
Net gain xi–2 98 498 998
Chapter 9
Exercises 9.1
1.
1
x–9
21
x+9
2
2.
1
x–8
21
x+8
2
3.
1
x–7
21
x+3
2
1
21
2
1
1
15. (A) 1 (B) 2 (C) Does not exist (D) 2 16. (A) 4 (B) 4 (C) 4
(D) Does not exist 17. 2 18. 1.9 19. 0.5 20. 1.5 21. (A) 1 (B) 2
5 44. –8>15 45. 3 46. –2
47. f(x)
48. f(x)
49. f(x)
50. f(x)
x
,
x
,
x
,
51. (A) 1 (B) 1 (C) 1 (D) 1 52. (A) 2 (B) 2
57. (A) 1 (B)
–1 (C) Does not exist (D) Does not exist 58. (A) 1
(B) –1 (C) Does not exist (D) Does not exist 59. (A) Does not exist
(B) 1
1
li
x
,
ANSWERS
75. No; Does not exist 76. Yes; –4 77. Yes; 7>5 78. Yes; 1>2
79. No; 0 80. No; 9 81. 3 82. 5 83. 4 84. 4 85. –7 86. –4
e
lim
x
,
lim
91. (A)
F1x2=e50
if 0 …x…10
9x–40
if x710 (B)
F(x)
150
(C) All 3 limits are 50.
if 0 …x6300
x
S1
,
000 D1x2 does not exist because
x
,
96. (A)
300 +0.97(x–300) =0.97x+9 if 300 …x61,000
97. F1x2=
e
80,000
if xÚ4,000
li
m
x
S4
,
000
F(x)=80,000;
li
m
xS8
,
000
F(x)=80,000
li
m
li
m
Answers A-47
6
9
A-50 Answers
Copyright © Pearson Education, Inc.
37.1 billion kilowatts per year.
88. (A) (B) C(30) ≈819.4, C′(30) ≈–61.2
In 2030, 819.4 billion kilowatts
89. (A)
P
′
1
t
2
=12 –2t (B) P
1
3
2
=107; P′
1
3
2
=6. After 3 hours, the
Exercises 9.5
1.
x
1>2 2.
x
1>3 3.
x
–
5
4.
x
–
1
5.
x12
6.
x
–
10
7.
x
–1>4 8.
x
–1>5
9. 0 10. 0 11.
7x
4
x3
14. 9x
15. –3x–
16. –5x–6
6
5
23. 1.8x
5
24. 2
.
1
x2
25. x
3 26. x
3 27. 12 28. –
5
29. 2 30. –4
31. 9 32. –17 33. 2 34. –4 35. 4t–3 36. 5 –24t
2
3
2
5
0
.7 –8.8u
1
.
2
40. 9u3.
5
–3.1 41. 0.5 –3.3t
2
42. 0.6t
2
–3.1 43. –8
51. –9
t
–6>5+12
t
–5>2 53. –1
u
–6>5
55. –0.6x–3>2+6.4x–3+1 56. –8.4x–4+0.4x–5>3
f
1
2
f
1
2
f
1
2
y
y
f
1
2
f
1
2
f
1
2
x
59. (A)
f
′
1
x
2
=12x
–12x (B)
f
′
1
2
2
=72;
f
′
1
4
2
=720
(C)
y
=72x–127; y=720x–2,215 (D) x=–1, 0, 1
f
1
2
f
1
2
f
1
2
3
f
f
(C) 5.5 s 62. (A) y=f′(x)=80 –20x (B)
f
′102=80 ft>s;
f
2
(B)
f
′102=15 ft>s;
f
′132=–12 ft>s (C)
x
=1
s
, x=5
s
f
f
x
s
x
x
f
1
2
f
1
2
f
1
2
f
1
2
f
1
2
f
1
2
76. No 77. 8x–4 78. 8x–20 79. –20x–2 80. –50x–
3
81. –1
x
–4
x
–
3
83. False 84. False 85. True
(B) S
1
4
2
=120.84, S′
1
4
2
=60.24. After 4 months, sales are $120.84 million
and are increasing at the rate of $60.24 million per month. (C) S
1
8
2
=560.84,
S′182=171.92. After 8 months, sales are $560.84 million and are increasing
$1,000 spent on advertising. 92. x
1
5
2
=46; x′
1
5
2
=–7.2. When the price
1.5% per year.
94. (A) (B) In 2025, 46.1% of female high school
0.9% per year.
95. (A) –1.37 beats>min (B) –0.58 beats>min 96. (A) –0.2 parts per
million per mile (B) –0.02
5
parts per million per mile 97. (A) 25 items/hr
6. 1; 1.21 7. 100; 102.01 8. 25; 24.01 9. ∆x=3; ∆y=75;
∆y>∆x=25 10. ∆x=3; ∆y=105; ∆y>∆x=35 11. 20
12. 25 13. 20 14. 25 15. dy =
1
24x–3x
dx
x
x
2
20. dy =126x–1>22dx 21. (A) 12 +3∆x (B) 12 22. (A) 18 +3∆x (B) 18
x
2
+5
29. dy =–3; ∆y=–10
3 30. dy =–20; ∆y=–20.803
31. 120 in.3 32. 31.4 cm3
21
1
1
2
1
2
1
2
1
2
1
Dy
20.15 0.15
Dy
44. (A) p=50 –0.05x, domain: 0 …x…1,000
At a production level of 4,500 saws, revenue is decreasing at the rate of
A-52 Answers
(E) P1x2=35x – x2
49. (A)
x=500 (B) P
1
x
2
=176x–0.2x
2
–21,900 (C) x=440
(D) Break-even points: 1150,
25, 5002 and 1730,
39, 4202; x intercepts for
1
2
50. (A) x=200 (B) P
1
x
2
=35x–0.1x
2
–2,340 (C) x=17
5
x
$4,000
400
51. (A) R
1
x
2
=20x–x3>2
1
1
2
1
258,
1,016
2
1200
52. (A) R
1
x
2
=60x–2x3>2
181, 3,4052, 1631,
6,1552
8000
(C) 1713,
807,7032, 15,423,
1,376,2272 (D) $254 …p…$1,133
y
x
y
x
Chapter 9 Review Exercises
3. (A) 22 (B) 8 (C) 2 (D) –
5
(9.1) 4. 1.5 (9.1) 5. 3.5 (9.1)
9. (A) 2 (B) 3 (C) Does not exist (D) 3 (9.1) 10. (A) 4 (B) 4
(C) 4 (D) Does not exist (9.1) 11. (A) Does not exist (B) 3
x
25. (A) –3 (B) 6 (C) –2 (D) 3 (E) –11 26. x
–10x (9.5)
27. x–1>2–3=1
x
1>2–3 (9.5) 28. 0 (9.5)
29. –3
–3
2
33. 5 (9.6) 34. 6 (9.6) 35. ∆y=0.64; dy =0.6 (9.6)
36. (A) 4 (B) 6 (C) Does not exist (D) 6 (E) No (9.3)
44. 3
4 x–1>2–
6 x–3>2=3
41x
–5
62x3 (9.5)
46. –3
1
1
2
=2
y
50. x=–1.3401, 0.5771, 2.2630 (9.4) 51. {2.4824 (9.5)
52. (A) y=f′
1
x
2
=16x–4 (B) 44 ft/sec (9.5)
54. (A) The graph of g is the graph of f
shifted 4 units to the right, and the
(B) The graph of g′ is the graph of
f
′ shifted 4 units to the right, and
57. 1–∞,
–42h 1–4,
12h 11,
∞2 (9.3) 58. 1–∞,
∞2 (9.3)
59. 3–2,
24 (9.3) 60. (A) –1 (B) Does not exist (C) –2
61. (A)
2 (B) 0 (C) Does not exist (9.1) 62. (A) –1 (B) 1
(C) Does not exist (9.1)
66. (A) ∞ (B) –∞ (C) ∞ (9.3) 67. (A) 0 (B) 0
70. 2
x
–1 (9.4) 71. 1>(21x) (9.4) 72. Yes (9.4) 73. No (9.4)
74. No (9.4) 75. No (9.4) 76. Yes (9.4) 77. Yes (9.4)
81. Horizontal asymptote:
y
=1; vertical asymptotes:
x
=–2,
x
=1 (9.2)
y
x
x
graph of y=f
1
x
2
is smooth, but it has a vertical tangent. (9.4)
84. (A) lim
x
S1– f1x2=1;
lim
x
S1– f1x2=–1
(B) lim
x
S1– f1x2=–1;
Copyright © Pearson Education, Inc.
x
5
85. (A) 1 (B) –1 (C) Does not exist
x
180
87. (A) $179.90 (B) $180 (9.7) 88. (A)
C
1
100
2
=9,500; C′
1
100
2
=50.
1
2
1
2
1
1
2
1
1
2
P′
1
x
2
=23 –0.02x; P1x2=23 –0.01x–
9,000
x
;
1
2
1
1
1
Loss
92. N
1
9
2
=27; N′
1
9
2
=3.5; After
36.9 trillion cubic feet and is increas-
94. (A) (B) Fixed costs: $484.21; variable costs
98. (A) C
20
16
(B) C1T2=12T
150 +T
33. (A) P
10,000
(B) lim
tS∞10,000e–
0
.
08
t=0
34. 8.66 yr 35. 17.33 yr
36. 13.86 yr 37. 8.66%
e
e
r
t
=
l
n 2
ln 2
that most investments would be
2P=P
e
2=ert;
rt =
l
n
2;
x
positive number, the restric-
tions on t are reasonable in
the sense that the doubling
Chapter 10
Exercises 10.1
1. A=1,465.68 2. A=
6
,041.2
6
3. P=9,117.21 4. P=34,261.53
A 5 6,000e0.1t 12. A 5 4,000e0.08t
$7,000
16. r=0.04
100 2.704 81
1,000 2.716 92
ANSWERS
Answers A-55
32. 11+ex21–ex2–11–ex2ex
1
1+ex
2
2=
1
1+ex
2
2
33. 11+x2a1
xb–ln x
2=1+x–x ln x
2
x ln 2 58. –3x ln 3 59.
60. (1.30, 3.65), (12.71, 332,105.11) 61. (0.49, 0.49) 62. (6.41, 6.41),
(93.35, 93.35) 63. (3.65, 1.30), (332,105.11, 12.71) 64. (4.18, 1.43),
(5,503.66, 8.61) 67. $28,447/yr; $18,664/yr; $11,021/yr 68. $2,594/yr;
$2,231/yr; $1,919/yr 69.
A′
1
t
2
=5,000
1
ln 4
2
4t;
A′
1
1
2
=27,726 bacteria/hr
2
1
1
2
1
2
1
2
1
2
1
1
1
1
A-56 Answers
94. (A)
N′1t2=
1801t+42–180t
1
t+4
2
2=720
1
t+4
2
2
1
f
2
96. (A)
dp
=
1
0.1p+1
2
2=100
1
0.1p+1
2
2
1
2
1
f
1
2
1
2
1
2
1
2
1
1
2
63.
f
′1x2=13x–42112–1x–82132
1
3x–4
2
2; y=5x–13
1–2 ln 2
x=3 68.
f
′
1
x
2
=
1
2x–3
21
2x
2
+
1
x
–6
21
2
2
=6x
–6x–12;
x=–1,
2
69.
f
′1x2=1x
1
x2+1
2
2=1–x2
1
x2+1
2
2; x=–1, x=1
2
1
1
1
1
1
1
1
1
1
1
1
1
1
2
86. –4x81–2x
21
ln
8
2
87. 12x
2
+5
1
4x3+5x+7
2
ln 3 88. 2x
2
1
2x+16
2
$12.50. At a production level of 24 cell phones, total cost is increasing at the
46. 1
3 13w–72–2>3132=1
3
3
1
3w–7
2
2
3
x+4e
3
x=4
3x
1
x2+9
2
1
x2+9
2
3xa1
3
A-58 Answers
dR
y
3
2–3y
1