Exponential Models with Differential Equations
AP Calculus BC · Flashcards
AP CALCULUS BC · FLASHCARDS
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QUESTION
If
d
y
d
t
=
k
y
\frac{dy}{dt} = ky
d
t
d
y
=
k
y
, what is the value of
k
k
k
for decay?
QUESTION
Find the solution to
d
y
d
t
=
−
2
y
\frac{dy}{dt} = -2y
d
t
d
y
=
−
2
y
with initial condition
y
(
0
)
=
5
y(0) = 5
y
(
0
)
=
5
.
QUESTION
Which function represents exponential decay:
y
=
e
k
t
y = e^{kt}
y
=
e
k
t
or
y
=
e
−
k
t
y = e^{-kt}
y
=
e
−
k
t
?
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ANSWER
y
=
e
−
k
t
y = e^{-kt}
y
=
e
−
k
t
. Negative exponent causes exponential decrease over time.
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