Answer
$3$ years
Work Step by Step
Given $Q(t)\approx Q_{0}e^{-0.139t}$, (from part a.)
we want to find t for which $Q(t)=\displaystyle \frac{2}{3}Q_{0}$
$\displaystyle \frac{2}{3}Q_{0}=Q_{0}e^{-0.139t}$
$\displaystyle \frac{2}{3}=e^{-0.139t}\qquad/\ln(...)$
$\displaystyle \ln(\frac{2}{3})=-0.139t$
$t=\displaystyle \frac{\ln(\frac{2}{3})}{-0.139}\approx 3$ years
