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Exercises 2.2
separates if we divide by
P
and multiply by
dt
.
Z
1
P
dP
=
r
100
Z
dt
⇒
ln
P
=
r
100
t
+
C
⇒
P
(
t
)=
Ke
rt/
100
,
where
K
is the initial amount of money in the savings account,
K
= $1000, and
r
%isthe
interest rate,
r
= 5. This results in
P
(
t
) = 1000
e
5
t/
100
.
(2.7)
(a)
To determine the amount of money in the account after 2 years we substitute
t
=2into
equation (2.7), which gives
P
(2) = 1000
e
10
/
100
= $1105
.
17
.
(b)
To determine when the account will reach $4000 we solve equation (2.7) for
t
with
P
= $4000:
4000 = 1000
e
5
t/
100
⇒
e
5
t/
100
=4
⇒
t
=20ln4
≈
27
.
73 years
.
(c)
To determine the amount of money in the account after 3
1
2
years we need to determine
the value of each $1000 deposit after 3
1
2
years has passed. This means that the initial
$1000 is in the account for the entire 3
1
2
years and grows to the amount which is given
by
P
0
= 1000
e
5(3
.
5)
/
100
. For the growth of the $1000 deposited after 12 months, we take
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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