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

Appendix I Answers to Odd-Numbered Exercises A105
31. Pstd − M 1 Ce 2kt P(0)
0
P(t)
M
33. y − 2 5 s100 1 2td 2 40,000s100 1 2td23y2 ; 0.2275 kgyL
35. (b) mtyc (c) smtycdft 1 smycde 2ctym g 2 m 2 tyc 2
37. (b) Pstd −
M
1 1 MCe 2kt
Exercises 9.6 • page 631
1. (a) x − predators, y − prey; growth is restricted only by
predators, which feed only on prey.
(b) x − prey, y − predators; growth is restricted by carrying
capacity and by predators, which feed only on prey.
3. (a) Competition
(b) (i) x − 0, y − 0: zero populations
(ii) x − 0, y − 400: In the absence of an x-population, the
y-population stabilizes at 400.
(iii) x − 125, y − 0: In the absence of a y-population, the
x-population stabilizes at 125.
(iv) x − 50, y − 300: Both populations are stable.
5. (a) The rabbit population starts at about 300, increases to 2400,
then decreases back to 300. The fox population starts at 100,
decreases to about 20, increases to about 315, decreases to 100,
and the cycle starts again.
(b) R
F
7.
2500
2000
1500
1000
500
0 t¡ t t£
t
Species 2
200
150
100
50
R
F
t=3
t=2
t=4
t=0, 5
t=1
300
200
100
0 50 100 150 200 250 Species 1
11. (a) Population stabilizes at 5000.
(b) (i) W − 0, R − 0: Zero populations
(ii) W − 0, R − 5000: In the absence of wolves, the rabbit
population is always 5000.
(iii) W − 64, R − 1000: Both populations are stable.
(c) The populations stabilize at 1000 rabbits and 64 wolves.
t
(d)
R
1500
1000
500
W
R
0 t
Chapter 9 Review • page 634
True-False Quiz
1. True 3. False 5. True 7. True
Exercises
1. (a)
(iv)
(iii)
(ii)
(i)
y
6
4
2
W
80
60
40
20
0 1 t
(b) 0 < c < 4; y − 0, y − 2, y − 4
y
3. (a)
_3
_2
_1
3
2
1
0 1 2 3 x
(b) 0.75676
(c) y − x and y − 2x; there is a loc max or loc min
5. y − s 1 2 x 2 1 Cde 2sin x
ys0.3d < 0.8
7. y − 6slnsx 2 1 2x 3y2 1 Cd
9. rstd − 5e t2t 2 11. y − 1 2 xsln xd2 1 2x 13. x − C 2 1 2 y2
2000
15. (a) Pstd −
1 1 19e ; <560 20.1t (b) t − 210 ln 2 57 < 33.5
17. (a) Lstd − L` 2 fL` 2 Ls0dge 2kt (b) Lstd − 53 2 43e 20.2t
19. 15 days 21. k ln h 1 h − s2RyVdt 1 C
23. (a) Stabilizes at 200,000
(b) (i) x − 0, y − 0: Zero populations
(ii) x − 200,000, y − 0: In the absence of birds, the insect
population is always 200,000.
(iii) x − 25,000, y − 175: Both populations are stable.
(c) The populations stabilize at 25,000 insects and 175 birds.
(d)
x (insects)
(birds) y
45,000
250
35,000
25,000
birds 200
150
15,000
insects
100
5,000
50
0 t
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