SOLUTION: carl plans to invest $500 at 8.25% INTREST, COMPOUNDED CONTINUOUSLY. how long will it take for his money to triple? use y= Pe^rt. show your work

Question 242151: carl plans to invest $500 at 8.25% INTREST, COMPOUNDED CONTINUOUSLY. how long will it take for his money to triple? use y= Pe^rt. show your work
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
After tripling $500 we will have $1500. So the equation we have to solve is:

First we'll divide both sides by 500:

Now, since the variable is up in the exponent, we will use logarithms to solve for it. The natural choice (excuse the pun) is to use natural logarithms (aka ln) because e is the base:

Using the property of logarithms, , we can move the exponent in the argument out in front as a coefficient:

Since by definition we now have:

Divide both sides by 0.0825:

This is an exact answer. You can use your calculator to find a decimal approximation for t (which is the time it will take to triple your money).

If your calculator doesn't "do" ln, we can use base 10 logs instead of ln:

Since we used base 10 logs, log(e) will not "disappear" like ln(e). So we are "stuck" with it. Divide both sides by 0.0825log(e):
(e is approximately equal to 2.7182818284590451. Round this off as you choose and then use your calculator to find t.

Although and do not look the same they are actually equal.

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