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Mathematics
Mathematics
Problem
A bacterial population covering a circular petri dish of area
A
(
mm
2
)
A\,(\text{mm}^2)
A
(
mm
2
)
satisfies
P
(
A
)
=
2000
ln
A
P(A)=2000\ln A
P
(
A
)
=
2000
ln
A
. The dish radius grows with time according to
r
(
t
)
=
50
+
2
t
r(t)=50+2t
r
(
t
)
=
50
+
2
t
millimeters, where
t
t
t
is measured in hours, and
A
=
π
r
2
A=\pi r^{2}
A
=
π
r
2
. Compute
d
P
d
t
\dfrac{dP}{dt}
d
t
d
P
at
t
=
1
h
t=1\text{ h}
t
=
1
h
.
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