Answer
The time taken is $18.5$ hours.
Work Step by Step
Let us consider the equation
$A={{A}_{o}}{{e}^{kt}}$
After a half-life, the amount becomes half
$\begin{align}
& \frac{{{A}_{o}}}{2}={{A}_{o}}{{e}^{kt}} \\
& \frac{1}{2}={{e}^{kt}} \\
& \ln 0.5=k\times 36 \\
& k=-1.92\times {{10}^{-2}}
\end{align}$
And the amount of Xanax after time t is $\frac{7{{A}_{o}}}{10}$.
$\begin{align}
& \frac{7{{A}_{o}}}{10}={{A}_{o}}{{e}^{kt}} \\
& \frac{7}{10}={{e}^{kt}} \\
& \ln \frac{7}{10}=-1.92\times {{10}^{-2}}t \\
& t=18.53
\end{align}$
Thus, approximately $18.5$ hours will be taken by the drug.
