Answer
The average increase is approximately $137$ per year from $1994$ through $1998$.
Work Step by Step
The values of the number of discharges for the year $1994$ is $617$.
The values of the number of discharges for the year $1998$ is $1163$.
Substitute the values $\left( {{x}_{2}},{{x}_{1}} \right)=\left( 1998,1994 \right)$ and $\left( f\left( {{x}_{2}} \right),f\left( {{x}_{1}} \right) \right)=\left( 1163,617 \right)$ to get the rate of change:
$\begin{align}
& \frac{\Delta y}{\Delta x}=\frac{f\left( {{x}_{2}} \right)-f\left( {{x}_{1}} \right)}{{{x}_{2}}-{{x}_{1}}} \\
& \frac{\Delta y}{\Delta x}=\frac{1163-617}{1998-1994} \\
& \frac{\Delta y}{\Delta x}=136.5 \\
& \frac{\Delta y}{\Delta x}\approx 137
\end{align}$
Therefore, the average rate of change rounded to a whole number from $1994$ through $1998$ is $137$.
