Answer
$\approx 2360$ million years
Work Step by Step
A decay model has the form $Q(t)=Q_{0}e^{-kt}$.
The decay constant k and half-life $t_{h}$ are related by
$t_{h}k=\ln 2$
Substitute $t_{h}=710$ and solve for k.
$710k=\ln 2$
$k=\displaystyle \frac{\ln 2}{710}\approx 0.0009763$
So,
$Q(t)\approx Q_{0}e^{-0.0009763t}$
Now, $Q_{0}=10$ g, $Q(t)=1$ g. Substituting, we solve for t.
$1=10e^{-0.0009763t}\qquad/\div 10$
$e^{-0.0009763t}=0.1\qquad/\ln(..)$
$-0.0009763t=\ln(0.1)$
$ t=\displaystyle \frac{\ln 0.1}{-0.0009763}\qquad$ ... round to 3 sig.dig.
$\approx 2360$ million years
