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Mathematics
Problem
A bacteria culture has population
N
(
t
)
N(t)
N
(
t
)
with
N
(
0
)
=
500
N(0)=500
N
(
0
)
=
500
. For
0
≤
t
<
4
0\le t<4
0
≤
t
<
4
hours,
d
N
d
t
=
0.3
N
\dfrac{dN}{dt}=0.3N
d
t
d
N
=
0.3
N
. For
4
≤
t
≤
10
4\le t\le10
4
≤
t
≤
10
hours, the growth constant changes so that
d
N
d
t
=
k
2
N
\dfrac{dN}{dt}=k_2N
d
t
d
N
=
k
2
N
. If
N
(
10
)
=
4000
N(10)=4000
N
(
10
)
=
4000
, what is the value of
k
2
k_2
k
2
(in h
−
1
^{-1}
−
1
)? a)
0.25
h
−
1
0.25\,\text{h}^{-1}
0.25
h
−
1
b)
0.15
h
−
1
0.15\,\text{h}^{-1}
0.15
h
−
1
c)
0.10
h
−
1
0.10\,\text{h}^{-1}
0.10
h
−
1
d)
0.21
h
−
1
0.21\,\text{h}^{-1}
0.21
h
−
1
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