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Mathematics
Mathematics
Problem
For a quantity that changes according to
d
y
d
t
=
k
y
\dfrac{dy}{dt}=ky
d
t
d
y
=
k
y
with initial condition
y
(
0
)
=
y
0
y(0)=y_0
y
(
0
)
=
y
0
, which of the following expresses the relationship between
y
y
y
and
t
t
t
as a linear equation in
t
t
t
? a)
y
=
y
0
+
k
t
y= y_0 + kt
y
=
y
0
+
k
t
b)
ln
y
=
y
0
+
k
t
\ln y = y_0 + kt
ln
y
=
y
0
+
k
t
c)
ln
y
=
ln
y
0
+
k
t
\ln y = \ln y_0 + kt
ln
y
=
ln
y
0
+
k
t
d)
y
=
y
0
e
k
t
y = y_0 e^{kt}
y
=
y
0
e
k
t
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