Question 898557
Your decay equation is A=Ao*e^(-0.001211t) in pure text and using your same variables.  This will appear more conventionally as {{{A=Ao*e^(-0.001211t)}}}.


You are given a relationship between A and Ao, and are asked for t.  Solve first symbolically for t, which is a more comfortable process.


{{{ln(A)=ln(Ao)+ln(e^(-0.001211t))}}}
{{{ln(A)=ln(Ao)+(-0.001211t)*1}}}
{{{ln(A)-ln(Ao)=-0.001211t}}}
{{{ln(Ao)-ln(A)=0.001211t}}}
{{{highlight_green(t=(1/0.001211)ln(Ao/A))}}}


You were given A is a percentage of Ao, so take Ao as 100 and A as 39.
Now just substitute into the formula for t:
{{{t=(1/0.001211)ln(100/39)}}}
...with a calculator for help....
{{{highlight(t=778)}}} years.



This showed at four significant figures to be 777.5 years, but how accurately you can trust the decay equation can be debated.  You most likely made a decimal mistake in your steps.