AP Calculus BC Quiz
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DIFFERENTIAL EQUATIONS
Question 1
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A quantity satisfies
d
y
d
t
=
2
3
y
\frac{dy}{dt}=\frac{2}{3}y
d
t
d
y
=
3
2
y
with
y
(
0
)
=
27
y(0)=27
y
(
0
)
=
27
. Which is
y
(
t
)
y(t)
y
(
t
)
?
A
27
e
2
t
/
3
27e^{2t/3}
27
e
2
t
/3
B
2
3
e
27
t
\frac{2}{3}e^{27t}
3
2
e
27
t
C
27
e
3
t
/
2
27e^{3t/2}
27
e
3
t
/2
D
27
(
2
3
)
t
27\left(\frac{2}{3}\right)^t
27
(
3
2
)
t
E
27
+
2
3
t
27+\frac{2}{3}t
27
+
3
2
t
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