Question

A = Pe^rt

Answer 1

That is the formula for solving for continuously compound interest.
You want to solve for time "t".
A = Pe^rt
Dividing both sides by "P"
(A / P) = e^r*t
Taking NATURAL LOGS of both sides:
(the natural log of "e" is 1)
ln (A / P) = ln (e^r*t)
ln (A / P) = r*t*1
ln (A / P) = rate * time
Time = ln (A / P) ÷ rate