Answer
Over $[5,6],\ 8.85$ manatee deaths per $100,000$ boats
Over $[7,8],\ 23.05$ 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 $[5,6]$,
Average rate of change = $\displaystyle \frac{f(6)-f(5)}{6-5}=\frac{27.6-18.75}{1}$
$\approx 8.85$ manatee deaths per $100,000$ boats
Over $[7,8]$,
Average rate of change = $\displaystyle \frac{f(8)-f(7)}{8-7}=\frac{66.6-43.55}{1}$
$\approx 23.05$ manatee deaths per $100,000$ boats
