How many years will it take for a $50 investment to grow to $5000 if it is compounded continuously at a rate of 5%? round to two decimal places. do not include unit in your answer. a(t)=p*e^rt

For one thing, you need that formula solved for years.
Also, for continuously compounded interest, a different formula is needed. It is located here:
http://www.1728.org/rate2.htm

Years = ln (total / principal) / rate
Years = ln (5,000 / 50) / .05
Years = ln (100) / .05
Years = 4.605170186 / .05
Years = 92.10340372
Years = 92.10 (rounded)

Here's a calculator to check that:
http://www.1728.org/compint.htm

What exactly is your question?