Answer
$f(t)=300\left(0.5^{x}\right)$
After 5 hours, $9.375$ mg remain.
Work Step by Step
We are given two points, (0,300) and (2,75)
and we want the model to have the form
$f(t)=Ab^{t}$
$\left[\begin{array}{lll}
\text{point on} & \text{corresponding} & \\
\text{the graph} & \text{equation} & \\
(0,300) & 300=Ab^{0} & \Rightarrow A=300\\
(2,75) & 75=Ab^{2} & \Rightarrow 75=300b^{2}\\
& &
\end{array}\right]$
so
$b=\displaystyle \left(\frac{75}{300}\right)^{1/2}=0.5$
The model is
$f(t)=300\left(0.5^{x}\right)$
$f(5)=300\left(0.5^{5}\right)=9.375$ mg
