SOLUTION: 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 i

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Question 65664: 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? what does "e" mean?
Found 2 solutions by Earlsdon, Edwin McCravy:
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Ok, starting with the given formula:
you need to solve this for t since you want to find the number of years, t.
The e in the formula is the base of natural logarithms, e = 2.71828... but you won't need to use the numerical value in solving this problem.
You are given:
A = $1,700
P = $1,000
r = 0.0442
Let's first solve the formula for t.
Divide both sides by P.
Now take the natural log of both sides.
Apply the "power rule" for logarithms to the right side: and recalling that you can simplify the right side to:
Divide both sides by r.
Now all you have to do is substitute the given values for A, P, and r and evaluate.

Use your calculator or a table of natural logs to find
years.
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!
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? 
-----------------------------------
>Yes, but you also need A = 1700

A = Pert

Substitute: 

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

Solve for t

A = Pert
1700 = 1000e.0442t

Divide both sides by 1000

1700/1000 = e.0442t

1.7 = e.0442t

Use the fact that any equation of the form

Y = eX

can be written as

X = ln(Y)

to rewrite

1.7 = e.0442t

as

.0442t = ln(1.7)

t = ln(1.7)/.0442

Get your calculator and find the ln key:

t = .530628251/.0442

t = 12.00516405

or about 12 years.

--------------------

what does "e" mean?
>
--------------------

"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, ln means loge

Edwin
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