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Mathematics
Problem
For a logistic model
d
Q
d
t
=
k
Q
(
L
−
Q
)
\dfrac{dQ}{dt}=kQ(L-Q)
d
t
d
Q
=
k
Q
(
L
−
Q
)
with
k
,
L
>
0
k,L>0
k
,
L
>
0
, let
G
(
Q
)
=
d
Q
d
t
G(Q)=\dfrac{dQ}{dt}
G
(
Q
)
=
d
t
d
Q
. A student differentiates
G
G
G
with respect to
t
t
t
and finds
d
G
d
t
=
k
2
Q
(
L
−
Q
)
(
L
−
2
Q
)
\dfrac{dG}{dt}=k^{2}Q(L-Q)(L-2Q)
d
t
d
G
=
k
2
Q
(
L
−
Q
)
(
L
−
2
Q
)
. For which value of
Q
Q
Q
does
G
G
G
change from increasing to decreasing? a)
3
L
4
\dfrac{3L}{4}
4
3
L
b)
L
2
\dfrac{L}{2}
2
L
c)
L
L
L
d)
L
4
\dfrac{L}{4}
4
L
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