The amount A in an account after t years from an initial principle P invested at an annual rate r compounded?

Question

continuously is given by A=Pe^rt where r is expressed as a decimal. Solve this formula for t in terms of A,P, and r.

Answer 1

A=Pe^rt
A/P = e^rt
ln (A/P) = rt
t = ln(A/P)/r

Answer 2

P=A/e^rt and
ln(P/A)= r*t so r=ln(P/A) /t