Answer
The average decrease is approximately $-130$ per year from $2001$ through $2006$.
Work Step by Step
The values of the number of discharges for the year $2001$ is $1273$.
The values of the number of discharges for the year $2006$ is $623$.
Substitute the values $\left( {{x}_{2}},{{x}_{1}} \right)=\left( 2006,2001 \right)$ and $\left( f\left( {{x}_{2}} \right),f\left( {{x}_{1}} \right) \right)=\left( 623,1273 \right)$ to get the rate of change:
$\begin{align}
& \frac{\Delta y}{\Delta x}=\frac{f\left( {{x}_{2}} \right)-f\left( {{x}_{1}} \right)}{{{x}_{2}}-{{x}_{1}}} \\
& \frac{\Delta y}{\Delta x}=\frac{623-1273}{2006-2001} \\
& \frac{\Delta y}{\Delta x}=-130
\end{align}$
Therefore, the average rate of change rounded to a whole number from $2001$ through $2006$ is $-130$.
