Exponential Growth Word problem

Question

Suppose that $50,000 from a retirement account is invested in a large cap stock fund. After 20 years, the value is $194,809.67.

a. Use the model A=Pe^rt to determine the average rate of return under continuous compounding. Round to the nearest tenth of a percent.

b. How long will it take the investment to reach one-quarter million dollars? Round to the nearest tenth of a year.

I have part a, and got 6.8%. Now, all I need help with is part b.

Answer 1

A(t) = Pe^rt

$250,000 = $50,000·e^0.068t

5 = e^0.068t

ln(5) = 0.068t

Solve for t. Use your calculator to get the numerical answer. Round to the nearest tenth as instructed.