Answer
Over $[5,7],\ 12.4$ manatee deaths per $100,000$ boats
Over $[6,8],\ 19.5$ manatee deaths per $100,000$ boats
Work Step by Step
The average rate of change of $f$ over the interval $[a, b]$ is
Average rate of change of $f\displaystyle \ \ =\frac{f(b)-f(a)}{b-a}$
The units of the average rate of change of $f$ are units of $f(x)$ per unit of $x$.
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Over $[5,7]$,
Average rate of change = $\displaystyle \frac{f(7)-f(5)}{7-5}=\frac{43.55-18.75}{2}$
$\approx 12.4$ manatee deaths per $100,000$ boats
Over $[6,8]$,
Average rate of change = $\displaystyle \frac{f(8)-f(6)}{8-6}=\frac{66.6-27.6}{2}$
$\approx 19.5$ manatee deaths per $100,000$ boats
