The rate of u. s. per capita sales of bottled water for the period 2000-2010 can be approximated by
s(t) = −0.18t^2 + 3t + 15 gallons per year (0 ≤ t ≤ 10),
where t is the time in years since the start of 2000.† after conducting a survey of sales in your state, you estimate that consumption in gyms accounts for a fraction
f(t) = √(0.2 + 0.04t)
of all bottled water consumed in year t. assuming your model is correct, estimate, to the nearest gallon, the total amount of bottled water consumed per capita in gyms from the start of 2007 to the start of 2010. hint
[rate of consumption = s(t)f(t).]

If p(x) is the total value of the production when there are x workers in a plant, then the average productivity of the workforce at the plant is a(x) = p(x) x . (a) find a'(x). a'(x) = xp'(x) − p(x) x a'(x) = xp'(x) − p(x) x2 a'(x) = p'(x) − p(x) x a'(x) = xp'(x) − p'(x) x2 a'(x) = p'(x) − xp(x) x2 why does the company want to hire more workers if a'(x) > 0? a'(x) > 0 ⇒ a(x) is ; that is, the average productivity as the size of the workforce increases. (b) if p'(x) is greater than the average productivity, which of the following must be true? p'(x) − xp(x) > 0 p'(x) − xp(x) < 0 xp'(x) − p'(x) > 0 xp'(x) − p(x) < 0 xp'(x) − p(x) > 0