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Mathematics
Problem
The quantity
Q
Q
Q
satisfies
d
Q
d
t
=
k
Q
\dfrac{dQ}{dt}=kQ
d
t
d
Q
=
k
Q
with initial amount
Q
0
Q_0
Q
0
. Which of the following expressions gives the time
t
t
t
required for the quantity to reach
5
Q
0
5Q_0
5
Q
0
? a)
t
=
5
k
t=\dfrac{5}{k}
t
=
k
5
b)
t
=
ln
5
k
t=\dfrac{\ln 5}{k}
t
=
k
ln
5
c)
t
=
k
ln
5
t=k\,\ln 5
t
=
k
ln
5
d)
t
=
ln
(
5
k
)
t=\ln(5k)
t
=
ln
(
5
k
)
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