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Mathematics
Mathematics
Problem
A population
P
(
t
)
P(t)
P
(
t
)
(in thousands) satisfies
d
P
d
t
=
k
P
\dfrac{dP}{dt}=kP
d
t
d
P
=
k
P
. It was
20
000
20\,000
20
000
at
t
=
3
t=3
t
=
3
years and
32
000
32\,000
32
000
at
t
=
7
t=7
t
=
7
years. (i) Determine the value of
k
k
k
(correct to three decimal places). (ii) Find
P
(
0
)
P(0)
P
(
0
)
. a. (i) Determine
k
k
k
.
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