James Stewart-Calculus_ Early Transcendentals-Cengage Learning (2015)

A104 Appendix I Answers to Odd-Numbered Exercises
43. (a) Cstd − sC 0 2 rykde 2kt 1 ryk (b) ryk; the concentration
approaches ryk regardless of the value of C 0
45. (a) 15e 2ty100 kg (b) 15e 20.2 < 12.3 kg
47. About 4.9% 49. tyk
51. (a) L 1 − KL2 k (b) B − KV 0.0794
53. (a) dAydt − ksA sM 2 Ad (b) Astd − MS Ce sM kt 2
2 1
,
Ce sM kt 1 1D
sM 1 sA0
where C − and A 0 − As0d
sM 2 sA 0
Exercises 9.4 • page 617
1200
1. (a) 1200; 0.04 (b) Pstd −
20.04t
(c) 87
1 1 19e
3. (a) 100; 0.05 (b) Where P is close to 0 or 100;
on the line P − 50; 0 , P 0 , 100; P 0 . 100
(c)
P
150
P¸=140
P¸=120
100
P¸=80
P¸=60
50
P¸=40
P¸=20
0 20 40 60 t
Solutions approach 100; some increase and some decrease, some
have an inflection point but others don’t; solutions with P 0 − 20
and P 0 − 40 have inflection points at P − 50
(d) P − 0, P − 100; other solutions move away from P − 0 and
toward P − 100
5. (a) 3.23 3 10 7 kg (b) <1.55 years 7. 9000
9. (a) dP − 1
dt 305 P S1 2
20D
P
(b) 6.24 billion (c) 7.57 billion; 13.87 billion
y 0
11. (a) dyydt − kys1 2 yd (b) y −
y 0 1 s1 2 y 0de 2kt
(c) 3:36 PM
15. P Estd − 1909.7761s1.0796d t 1 94,000;
33,086.4394
P Lstd −
1 94,000
1 1 12.3428e 20.1657t
130,000
(d)
P
1200
800
400
0 40 80 120 t
ty25
250 2 750ke
(e) Pstd −
1 2 ke ty25
where k − 1 11 , 2 1 9
21. (b)
P
1400
1200
1000
800
600
400
200
P 1200
0 20 40 60 80 100 t
0 , P 0 , 250: P l 0;
P 0 − 250: P l 250;
P 0 . 250: P l 750
0 120
t
0 , P 0 , 200: P l 0;
P 0 − 200: P l 200;
P 0 . 200: P l 1000
sM2mdskyMdt
msM 2 P0d 1 MsP0 2 mde
(c) Pstd −
M 2 P 0 1 sP 0 2 mde sM2mdskyMdt
23. (a) Pstd − P 0e skyrdfsinsrt 2 d 1 sin g (b) Does not exist
Exercises 9.5 • page 625
1. No 3. Yes 5. y − 1 1 Ce 2x
7. y − x 2 1 1 Ce 2x 9. y − 2 3 sx 1 Cyx
11. y − x 2 sln x 1 Cd 13. y − 1 3 t23 s1 1 t 2 d 3y2 1 Ct 23
15. y − 1 x ln x 2 1 x 1 3 x 2 17. u − 2t 2 1 t 3
19. y − 2x cos x 2 x
21. y − sx 2 1de x 1 C
x 2
C=3
C=5
C=7
5
C=3
C=5
C=7
P
P L
P E
t (in years)
_3
C=1
3
90,000
1960
2010
17. (a) Pstd − m k 1 SP 0 2 m kDe kt (b) m , kP 0
(c) m − kP 0, m . kP 0 (d) Declining
19. (a) Fish are caught at a rate of 15 per week.
(b) See part (d). (c) P − 250, P − 750
25. y − 6SCx 4 1
5xD
2 21y2
C=_5
C=_3
C=_1
_5
C=_5
C=_3
C=_1
6et Ans. 9.5.21
12.07.06
27. (a) Istd − 4 2 4e 25t (b) 4 2 4e 21y2 < 1.57 A
29. Qstd − 3s1 2 e 24t d, Istd − 12e 24t
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