Question

The amount of water remaining in the pool is decreasing at a rate of

Answer 1

The average rate of change has a relationship with slopes. In this way, we can write the slope of a line as follows:

$Slope=\frac{Change \ y}{Change \ x}$

As you can see in the graph, we have a straight line whose slope is negative. This slope as we have said is the Average Rate of Change we need to find. So, to find the slope of this line we must choose two points and compute the following formula:

$ARC=Slope=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}$

The two points can be:

$P_{1}(0,40) \ and \ P_{2}(10,0)$

So:

$ARC=\frac{0-40}{10-0} \\ \\ \therefore \boxed{ARC=-4 \ gallons \ per \ minutes}$

Finally, the conclusion is:

The amount of water remaining in the pool is decreasing at a rate of 4 gallons per minute