Question 1192687
Nf=Noe^(-kt)
(1/2)=e^(-kt) for half life
ln(1/2)=(-5730k)
-0.693=-5730k
k=0.0001210
now Nf/No=0.13
so 0.13=e^(-0.0001210t)
ln both sides to remove e
-2.040=-0.0001210t
t=16,861 years.
13% is not quite 3 half lives (12.5% is), which is 17,190 years, so the answer makes sense.