The amount of water in a storage tank, in gallons, is modeled by a continuous function on the time interval 0<=t<=7, where t is measured in hours. In this model, rates are give as:
(i)The rate at which water enters the tank is f(t)=100t^2*sin(sqrt(t))
(ii) The rate at which water leaves the tank is
g(t)=250 for 0<=t<3 gallons/hour
g(t)=2000 for 3<t<=7 gallons/hour
The graphs of f and g intersect at t=1.617 and 5.076. At time t=0, the amount of water in the tank is 5000 gallons.
a. For 0<=t<=7, find the time intervals during which the amount of water in the tank is decreasing.
b. For 0<=t<=7, at what time t is the amount of water in the tank greatest ? To the nearest gallon, compute the amount of water at this time.
The Attempt at a Solution
a. I got 2 intervals: 3<t<5.076 and 0<t<1.617 because g(t) >f(t) in these two intervals. Am I right ??
b. How should I do part b ?? I kinda get the idea in my head that g(t) should be as small as possible and f(t) has to be as big as possible. Can anyone give me a hint ??