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Sec.
5.3 –
Logarithms and Their Properties
First, let’s do a little preliminary investigation! In the last section we used
the exponential formula :
1
nt
r
A
P
n
=
+
Now in this formula, there are 5
variables. Right??
A, P, r, n, and t.
Now if we are given any four of these
values, we should be able to solve for the fifth one.
Let’s see: we did the case where we knew P, r, n, and t and solved for A.
Suppose I want to
end up
with $5000 after 3 years and I can get 6% interest,
compounded monthly. How much money would I have to put into the
account to end up with $5000??
(12)(3)
.06
5000
1
12
P
=
+
(
29
36
5000
1 .005
P
=
+
(
29
36
5000
1.005
P
=
(
29
36
5000
1.005
P
=
4178.22
P
=
So yes we can find P.
But suppose I only have $4000 to put in savings. That will not grow to
$5000 in 3 years at 6%. So I need to find an account giving better than a 6%
rate. What rate do I need??
(12)(3)
5000
4000 1
12
r
=
+
can we find r??
36
5000
1
4000
12
r
=
+
36
1.25
1
12
r
=
+
36
1.25
1
12
r
= +
36
1.25 1
12
r
 =
36
12( 1.25 1)
r

=
.0746
r
=
So I need about 7.5% interest rate.
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View Full DocumentNow suppose I want to put $4000 in an account and have it grow to $5000
and the rate is 6% compounded monthly. Question is how long will it take to
grow to $5000. What is the value of “t”??
(12)
.06
5000
4000 1
12
t
=
+
Can we find “t”??
(
29
12
5000
4000 1.005
t
=
(
29
12
5000
1.005
4000
t
=
(
29
12
1.25
1.005
t
=
Now, what can we do to get t by itself???
Similar to asking, in
17
3
x
=
what can we do to get
x
by itself ???
We have
nothing
at our command to solve this equation!! We can’t add
something to both sides, subtract something on both sides, multiply, divide,
take a root, raise to a power    nothing helps. We need help!! And help is
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 Spring '10
 stean

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