Answer
The average rate of change is $-\$4000$.
The value of the machine depreciates at an average of $\$4000$ per year.
Work Step by Step
The graph is from $x=0$ to $x=4$ so the interval is $[0, 4]$.
RECALL:
The average rate of change in the interval $[a, b]$ is given by the formula:
average rate of change = $\dfrac{f(b)-f(a)}{b-a}$
The given graph has $f(0) = 20$ and $f(4) = 4$.
Thus, the average rate of change in the interval $[0, 4]$ is:
$=\dfrac{f(4)-f(0)}{4-0}
\\=\dfrac{4-20}{4}
\\=\dfrac{-16}{4}
\\=-4$
Therefore, the value of the machine depreciates at an average of $\$4000$ per year.