Page 184 - How To Solve Word Problems In Calculus

1
−0.4t = ln
4
0.4t = ln 4

ln 4
t = ≈ 3.47 months
0.4

(e) The fish population will be at 70 percent of the pond’s capacity
of 5000 when P (t) = 3500.

5000
3500 =
1 + 4e −0.4t
3500(1 + 4e −0.4t ) = 5000

10
1 + 4e −0.4t =
7

3
−0.4t
4e =
7
3
e −0.4t =
28
3
−0.4t = ln
28

28
0.4t = ln
3
28
ln
3
t = ≈ 5.58 months.
0.4

10. (a) The number of people who initially contracted the disease is

10 10
Q(0) = = ≈ 0.099 (in thousands)
1 + 100e 0 101

99 people initially contracted the disease.
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