Answer
$f(t)=200\left(0.5625^{x}\right)$
After 4 hours, the blood alcohol level is about $20.023$ mg/dL
Work Step by Step
We are given two points, (0,200) and (2,112.5)
and we want the model to have the form
$f(t)=Ab^{t}$
$\left[\begin{array}{lll}
\text{point on} & \text{corresponding} & \\
\text{the graph} & \text{equation} & \\
(0,200) & 200=Ab^{0} & \Rightarrow A=200\\
(2,112.5) & 112.5=Ab^{2} & \Rightarrow 112.5=200b^{2}\\
& &
\end{array}\right]$
so
$b=\displaystyle \left(\frac{112.5}{200}\right)^{1/2}=0.5625$
The model is
$f(t)=200\left(0.5625^{x}\right)$
$f(4)=200\left(0.5625^{4}\right)= 20.02258$ mg/dL
