Logistic Models with Differential Equations
AP Calculus BC · Flashcards · Application
AP CALCULUS BC · FLASHCARDS
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QUESTION
Calculate
P
(
t
)
P(t)
P
(
t
)
when
K
=
200
K = 200
K
=
200
,
r
=
0.2
r = 0.2
r
=
0.2
, and
P
(
0
)
=
100
P(0) = 100
P
(
0
)
=
100
. Use logistic solution.
QUESTION
Find
P
(
t
)
P(t)
P
(
t
)
when
r
=
0.5
r = 0.5
r
=
0.5
,
K
=
100
K = 100
K
=
100
, and
P
(
0
)
=
10
P(0) = 10
P
(
0
)
=
10
.
QUESTION
State the solution for
P
(
t
)
P(t)
P
(
t
)
when
P
(
0
)
=
K
2
P(0) = \frac{K}{2}
P
(
0
)
=
2
K
in logistic growth.
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ANSWER
P
(
t
)
=
K
1
+
e
−
r
t
P(t) = \frac{K}{1 + e^{-rt}}
P
(
t
)
=
1
+
e
−
r
t
K
. When
P
(
0
)
=
K
2
P(0) = \frac{K}{2}
P
(
0
)
=
2
K
, then
A
=
1
A = 1
A
=
1
in the solution.
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