[tex] \text{We need to find the average rate of change over the time interval }[0,4]\\
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\text{we know that the average rate of change of a function f(x) over interval }[a,b]\\
\text{is given by}\\
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f_{avg}=\frac{f(b)-f(a)}{b-a}\\
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\text{so using this concept the average rate of change over the given interval is}\\
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\text{average rate of change}=\frac{A(4)-A(0)}{4-0}\\
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\text{from the graph, we can see that at t=0 minutes, amount of water is 40 gallons} [/tex]
[tex] \text{and at t=4 minutes, the amount of water in the play pool is 24 gallons.}\\
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\text{Hence the average rate of change}=\frac{24-40}{4-0}\\
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=\frac{-16}{4}\\
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=-4 [/tex]
Hence average rate of change on the given time interval is: -4
