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Mathematics
Mathematics
Problem
A bacteria culture is modeled by
P
(
t
)
=
C
t
r
P(t)=C t^{r}
P
(
t
)
=
C
t
r
, where
P
(
t
)
P(t)
P
(
t
)
is the population after
t
t
t
hours,
C
>
0
C>0
C
>
0
, and
r
r
r
is a constant exponent. Measurements show
P
(
4
)
=
200
P(4)=200
P
(
4
)
=
200
and
P
′
(
4
)
=
75
P'(4)=75
P
′
(
4
)
=
75
. What is the value of
r
r
r
? a)
3
8
\dfrac{3}{8}
8
3
b)
8
3
\dfrac{8}{3}
3
8
c)
3
2
\dfrac{3}{2}
2
3
d)
2
2
2
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