Chapter 8.4, Problem 62PE

An investment grows exponentially under continuous compounding. After $2\text{ yr}$ , the amount in thee account is $\text{\$}\mathrm{7328.70.}$ After $5\text{ yr,}$ the amount in the account is $\text{\$}\mathrm{8774.10.}$ Use the model $A\left(t\right)=P{e}^{rt}$ to

a. Find the interest rate $r.$ Round to the nearest percent.

b. Find the original principal $P.$ Round the nearest dollar.

c. Determine the amount of time required for the account to reach a value of $\text{\$}15,000.$ Round to the nearest year.