Suppose that $$25,000$ from a retirement account is invested in a large cap stock fund. After $35yr,$ the value is $$165,817\mathrm{.}22.$

Part $1$ of $2$

$($a$)$ Use the model $A=P{e}^{rt}$ to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent. Avoid rounding in intermediate steps.

The average rate is approximately $\%$

Part: $\frac{1}{2}$

Part $2$ of $2$

$($b$)$ How long will it take the investment to reach one$-$quarter million dollars? Round to the nearest tenth of a year. Round values in intermediate steps to three decimal places.

it will take approximately years.