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Mathematics
Mathematics
Problem
A population
P
(
t
)
P(t)
P
(
t
)
satisfies
d
P
d
t
=
k
P
\dfrac{dP}{dt}=kP
d
t
d
P
=
k
P
. If
P
(
0
)
=
400
P(0)=400
P
(
0
)
=
400
and
P
(
5
)
=
600
P(5)=600
P
(
5
)
=
600
, determine the value of
k
k
k
and then find
P
(
12
)
P(12)
P
(
12
)
. Express both answers exactly.
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