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Mathematics
Problem
A population
P
(
t
)
P(t)
P
(
t
)
(in organisms) obeys
d
P
d
t
=
0.3
P
(
1
−
P
1000
)
\dfrac{dP}{dt}=0.3\,P\left(1-\dfrac{P}{1000}\right)
d
t
d
P
=
0.3
P
(
1
−
1000
P
)
with
P
(
0
)
=
100
P(0)=100
P
(
0
)
=
100
. Find an explicit expression for
P
(
t
)
P(t)
P
(
t
)
valid for
t
≥
0
t\ge 0
t
≥
0
.
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