Answer
$0.17\,\mu g$
Work Step by Step
Time elapsed=10.8 days=$\frac{10.8\,days}{2.69\,days}$ half-lives= 4.01 half-lives.
The amount of gold-198 has decreased to $(\frac{1}{2})^{4.01}$ of the original amount.
The amount of gold-198 remaining$=2.8\,\mu g\times(\frac{1}{2})^{4.01}=0.17\,\mu g$