Question

If the half-life of aspirin in the bloodstream is 5 hours, how much aspirin is left in the bloodstream 12 hours after 1000 milligrams is administered

Answer 1

`\bf \textit{Amount for Exponential Decay using Half-Life} \\\\ A=P\left( (1)/(2) \right)^{(t)/(h)}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &1000\\ t=\textit{elapsed time}\dotfill &12\\ h=\textit{half-life}\dotfill &5 \end{cases} \\\\\\ A=1000\left( (1)/(2) \right)^{(12)/(5)}\implies A\approx 1000\cdot 0.189\implies A\approx 189`