Chapter 14.1, Problem 62E

Bottled Water Sales The rate of U.S. sales of bottled water for the period 2000–2010 can be approximated by

$s\left(t\right)=-0.18t^2+3t+15\text{ gallons per year}\left(0\le t\le 10\right),$ where t is time in years since the start of 2000.⁷ After conducting a survey of sales in your state, you estimate that consumption in gyms accounts for a fraction.

$f\left(t\right)=\sqrt{0.2+0.04t}\text{.}$ ofall bottled water consumed in year t. Assuming that your model is correct, estimate, to the nearest gallon, the total amount of bottled water consumed per capita in gyms from the start of 2005 to the start of 2010. [HINT: Rate of consumption $=s\left(t\right)f\left(t\right)$. Also see Example 31.]