[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\
A=I(1 - r)^t\qquad
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
\end{cases}\\\\
-------------------------------\\\\
\textit{at 0 seconds, t = 0, the patient has 320mg in its blood}
\\\\\\
320=I(1-r)^0\implies 320=I\cdot 1\implies 320=I
\\\\\\
A=320(1-r)^t\\\\
-------------------------------\\\\[/tex]
[tex]\bf \textit{2 hours later, t = 2, the patient has 80mg in its blood}
\\\\\\
80=320(1-r)^2\implies \cfrac{80}{320}=(1-r)^2\implies \cfrac{1}{4}=(1-r)^2
\\\\\\
\sqrt{\cfrac{1}{4}}=1-r\implies \cfrac{\sqrt{1}}{\sqrt{4}}=1-r\implies \cfrac{1}{2}=1-r\implies r=1-\cfrac{1}{2}
\\\\\\
r=\cfrac{1}{2}\implies r=0.5\qquad A=320(1-0.5)^t\implies \boxed{A=320(0.5)^t}[/tex]
