Question

a new drug to treat a disease has a half life of 3 hours. if 50cc is initially administered, how much will still be in your system 24 hours later?

Answer 1

`\bf \textit{Amount for Exponential Decay using Half-Life}\\\\ A=I\left( (1)/(2) \right)^{(t)/(h)}\qquad \begin{cases} A=\textit{accumulated amount}\\ I=\textit{initial amount}\to &50\\ t=\textit{elapsed time}\to &24\\ h=\textit{half-life}\to &3 \end{cases} \\\\\\ A=50\left( (1)/(2) \right)^{(24)/(3)}\implies A=50\left( (1)/(2) \right)^8\implies A=50\cdot \cfrac{1^8}{2^8} \\\\\\ A=50\cdot \cfrac{1}{256}\implies A=\cfrac{50}{256}\implies A=\cfrac{25}{128}`