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2 2007 AP® CALCULUS AB FREERESPONSE QUESTIONS 2. 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 given as follows:
(i) The rate at which water enters the tank is f (t ) = 100t 2 sin ( t ) gallons per hour for 0 £ t £ 7.
(ii) The rate at which water leaves the tank is
g (t ) = { 250 for 0 £ t < 3
gallons per hour.
2000 for 3 < t £ 7 The graphs of f and g, which intersect at t = 1.617 and t = 5.076, are shown in the figure above. At time
t = 0, the amount of water in the tank is 5000 gallons.
(a) How many gallons of water enter the tank during the time interval 0 £ t £ 7 ? Round your answer to the
nearest gallon.
(b) For 0 £ t £ 7, find the time intervals during which the amount...
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 Spring '09
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