Exponential Models with Differential Equations
AP Calculus AB · Flashcards · Recall
AP CALCULUS AB · FLASHCARDS
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QUESTION
What is the general solution form for a differential equation
d
y
d
t
=
k
y
\frac{dy}{dt} = ky
d
t
d
y
=
k
y
?
QUESTION
What is the initial value in
N
(
t
)
=
N
0
e
−
λ
t
N(t) = N_0 e^{-\lambda t}
N
(
t
)
=
N
0
e
−
λ
t
?
QUESTION
For
d
y
d
t
=
k
y
\frac{dy}{dt} = ky
d
t
d
y
=
k
y
, determine
y
(
t
)
y(t)
y
(
t
)
if
y
0
=
12
y_0 = 12
y
0
=
12
.
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ANSWER
y
(
t
)
=
12
e
k
t
y(t) = 12e^{kt}
y
(
t
)
=
12
e
k
t
. General solution with specified initial value
y
0
=
12
y_0=12
y
0
=
12
.
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