Question

The drug lorazepam, used to relieve anxiety and nervousness, has a half life of 14 hours. if a doctor prescribes one 2.5 milligram tablet every 24 hours, then what percentage of the last dosage remains in the patients body when the next dosage is taken

Answer 1

$\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( \frac{1}{2} \right)^{\frac{t}{h}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &2.5\\ t=\textit{elapsed time}\dotfill &24\\ h=\textit{half-life}\dotfill &14 \end{cases} \\\\\\ A=2.5\left( \frac{1}{2} \right)^{\frac{24}{14}}\implies A=2.5\left( \frac{1}{2} \right)^{\frac{12}{7}}\implies A\approx 0.761883533878$