Precalculus (6th Edition) Blitzer

The time taken is $18.5$ hours.
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.