Question 65664
<pre>Ok I really need help. 
"The amount A is an account after t years from an initial principle P invested
at an annual rate r compounded continuously is given by A=Pe^rt where r is
expressed as a decimal. How many years will it take an an initial investment of
$1000 to grow to $1700 at the rate of 4.42% compunded continuously?" 
Ok, so far I have 
r=4.42/100=.0442
P=1000
t=? 
A=(1000)e^(.0442) (?) 
Do I have this right? 
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<font size = 5 color = "darkblue">><b>Yes, but you also need A = 1700

A = Pe<sup>rt</sup>

Substitute: 

A = 1700
r = .0442,
P = 1000
t = ?

Solve for t

A = Pe<sup>rt</sup>
1700 = 1000e<sup>.0442t</sup>

Divide both sides by 1000

1700/1000 = e<sup>.0442t</sup>

1.7 = e<sup>.0442t</sup>

Use the fact that any equation of the form

Y = e<sup>X</sup>

can be written as

X = <font face = "French Script MT" size = 6>ln</font>(Y)

to rewrite

1.7 = e<sup>.0442t</sup>

as

.0442t = <font face = "French Script MT" size = 6>ln</font>(1.7)

t = <font face = "French Script MT" size = 6>ln</font>(1.7)/.0442

Get your calculator and find the <font face = "French Script MT" size = 6>ln</font> key:

t = .530628251/.0442

t = 12.00516405

or about 12 years.

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what does "e" mean?
<font size = 5 color = "darkblue">><b>
--------------------

"e" is a special number, which you
will learn more about if you study
calculus.  Its value is about 2.718
but you need not be concerned with
it.  It is the base of natural 
logarithms, <font face = "French Script MT" size = 6>ln</font> means log<sub><font size = 6>e</font></sub>

Edwin</pre></font></b>