Question 82638
The amount A in an account after t years of an initial principle P invested at an annual rate r compounded continously 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.
:
{{{P*e^rt}}} = A; Find t
:
Divide both sides by P and you have:
{{{e^rt}}} = {{{A/P}}}
:
Use the nat logs, and log equivalent of exponents:
rt * ln(e) = ln(A/P)
:
nat log  of e = 1, so it's just:
r*t  = ln(A/P)
:
Divide both sides by r:
t = {{{(ln(A/P))/r}}}

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