A84
||||
APPENDIX H ANSWERS TO ODD-NUMBERED EXERCISES
41. 43.
45. 47.
49. 51.
55. 57. 59.
(b) 0.567143
61. (a) 1 (b)
(c)
63. 1 65.
,
67. (a) Inc. on ; dec. on
(b) CU on ; CD on (c)
69. A.
B. y-int. C. None
D. HA ; VA
E. Inc. on ,
F. None
G. CU on , ;
CD on ; IP
H. See graph at right
71. 28.57 min, when the rate of increase of drug level in the blood-
stream is greatest; 85.71 min, when rate of decrease is greatest
73. Loc. max. ;
loc. min. ;
IP
75. 77.
79. 81.
83. 85.
4.644 87. 91.
EXERCISES 7.4*
N
PAGE 445
1. (a) (b) (c)
(d) See Figures 1, 3, and 2.
3. 5.
7.
(a) 3 (b) 9. (a) 3 (b)
11. All approach 0 as ,
all pass through , and
all are increasing. The larg-
er the base, the faster the
rate of increase.
共0, 1兲
x l
共0.15, 1.15兲, 共1.09, 0.82兲
f
(
1兾
s
3
)
苷 e
2
s
3兾9
⬇ 0.7
f
(
1兾
s
3
)
苷 e
2
s
3兾9
⬇ 1.5
(
1
2
, 1兾e
2
)(
1
2
,
)
(
1,
1
2
)
共, 1兲
共1, 兲共, 1兲
x 苷 1y 苷 1
1兾e
kae
kt
兾共1 ae
kt
兲
2
f
共n兲
共x兲 苷 2
n
e
2x
4, 2
y 苷 共1 2xye
x
2
y
兲兾共x
2
e
x
2
y
1兲y 苷 2x 1
y 苷
4e
2x
共1 e
2x
兲
2
sin
1 e
2x
1 e
2x
y 苷
共ad bc兲e
x
共ce
x
d 兲
2
y 苷 e
e
x
e
x
y 苷 3e
3x
兾
s
1 2e
3x
13. (a) (b) (c)
15. All graphs approach
as , all pass
through , and all
are increasing. The
larger the base, the
slower the rate of
increase.
17. 19. (b) About 1,084,588 mi
21. 23. 0
25. 27.
29.
31. 33.
35. 37.
39.
41.
43. 45.
47.
49. 51.
53.
0.600967 55. 57. 8.3
59.
61.
(a) where and
(b) A
EXERCISES 7.5
N
PAGE 453
1. About 235
3. (a) (b) (c)
(d)
5. (a) 1508 million, 1871 million (b) 2161 million
(c) 3972 million; wars in the first half of century, increased life
expectancy in second half
7. (a) (b)
9. (a) (b) (c)
11. 13. (a) (b)
15. (a) (b)
17. (a) (b)
19. (a) (i) $3828.84 (ii) $3840.25 (iii) $3850.08
(iv) $3851.61 (v) $3852.01 (vi) $3852.08
(b) ,
EXERCISES 7.6
N
PAGE 461
1. (a) (b) 3. (a) (b)
5. (a) 10 (b) 7. 9.
13.
x兾
s
1 x
2
2
3
s
22兾
s
5
兾3
兾4
兾4
兾3
A共0兲 苷 3000dA兾dt 苷 0.05A
⬇39.9 kPa⬇64.5 kPa
⬇67.74 min13.3C
⬇116 min⬇ 137F⬇2500 years
⬇199.3 years⬇ 9.92 mg100 2
t兾30
mg
2000 ln 0.9 ⬇ 211 sCe
0.0005t
共ln 100兲兾共ln 4.2兲⬇3.2 h
⬇10,632 bacteria兾h⬇7409100共4.2兲
t
670.63
b ⬇ 0.000045146a ⬇ 100.01244y 苷 ab
t
10
8
兾ln 10 dB兾共watt兾m
2
兲
y 苷
1
10
x
1
16兾共5 ln 5兲 1兾共2 ln 2兲3
sin
兾ln 3 C
[
or
1
2
共ln 10兲共log
10
x兲
2
C
]
共ln x兲
2
兾共2 ln 10兲 C
90兾共ln 10兲y 苷 共10 ln 10兲x 10共1 ln 10兲
y 苷 共tan x兲
1兾x
冉
sec
2
x
x tan x
ln tan x
x
2
冊
y 苷 共cos x兲
x
共x tan x ln cos x兲
y 苷 x
sin x
冉
sin x
x
cos x ln x
冊
y 苷 x
x
共1 ln x兲
y 苷
1
ln 10
log
10
xf 共x兲 苷
3
共3x 1兲 ln 2
f 共u兲 苷 10 ln 2 共2
u
2
u
兲
9
共2
u
2
u
兲
y 苷 5
1兾x
共ln 5兲兾x
2
h共t兲 苷 3t
2
3
t
ln 3
f 共x兲 苷 3 ⴢ 2
x
共1, 0兲
x l 0