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Unformatted text preview: College Board. All rights reserved. Visit apcentral.collegeboard.com (for AP professionals) and www.collegeboard.com/apstudents (for students and parents). GO ON TO THE NEXT PAGE. -2- 2007 AP® CALCULUS AB FREE-RESPONSE 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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