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Exponential Growth and
Decay
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View Full Document Exponential Model
If
y(t)
is the value of a quantity at time
t
and if the rate
of change of
y
with respect to
t
is proportional to its
size
y(t)
at any time, then
ky
dt
dy
=
k
is a constant, called the constant of proportionality.
Comments
If
k
is positive, then the model represents natural or
exponential growth.
If
k
is negative, then the model represents natural or
exponential decay.
ky
dt
dy
=
This is a differential equation because it
involves
y
and its derivative.
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View Full Document Theorem
kt
e
y
t
y
)
0
(
)
(
=
The only solutions of the exponential model are the
exponential functions
kt
e
y
t
y
ky
dt
dy
)
0
(
)
(
:
s
other word
In
=
⇔
=
Example
1. Determine an differential equation for Q(t).
Exponential model:
kQ
dt
dQ
=
The rate at which a radioactive substance decays is
proportional to the amount Q(t) of the substance
remaining at time t.
2.
Find the solution of the equation, assuming
that initially there were 15 kg of the
substance and that its halflife is 120 years.
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This note was uploaded on 01/21/2011 for the course PHYS 4A 60865 taught by Professor L. oldewurtel during the Fall '09 term at Irvine Valley College.
 Fall '09
 L. OLDEWURTEL

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