Page 174 - How To Solve Word Problems In Calculus

−320e −2t (1 + 4e −2t )[1 + 4e −2t − 8e −2t ]
=
)
(1 + 4e −2t 4
−320e −2t (1 − 4e −2t )
=
)
(1 + 4e −2t 3

P (t) = 0 if and only if
1 − 4e −2t = 0
1 = 4e −2t

e 2t = 4
2t = ln 4
1
t = ln 4 ≈ 0.693 year
2
20
(e) P(t) = . As t →∞, e −2t → 0 so lim P(t) =
1 + 4e −2t t→∞
20 thousand deer.
(f ) 80 percent of 20,000 = 16,000 deer so we need to find t for
which P(t) = 16.
20
P(t) =
1 + 4e −2t
20
16 =
1 + 4e −2t
16(1 + 4e −2t ) = 20
5
1 + 4e −2t =
4
1
4e −2t =
4
1
e −2t =
16
e 2t = 16
2t = ln 16

1
t = ln 16 ≈ 1.39 years
2
161