Answer
a) $C(t)= 100\cdot (0.84)^t$
b) $41.82$ mg
Work Step by Step
The problem describes an exponential function with the following parameters.
\begin{equation}
\begin{aligned}
a&= 100\\
r&= 16\%= 0.16\\
b&=1-r = 0.84\\
\end{aligned}
\end{equation}
a) A model of the caffeine in the body as a function of time is given.
\begin{equation}
\begin{aligned}
C(t)&= a\cdot b^t\\
&= 100\cdot (0.84)^t\\
\end{aligned}
\end{equation}
b) Set $t= 5$.
\begin{equation}
\begin{aligned}
C(5)&= 100\cdot (0.84)^{5}\\
&= 41.82\\
\end{aligned}
\end{equation}
The amount of caffeine in the body after 5 hours is about $41.82$ mg.
