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2001 Free Response

# C a student proposes the function p given by p t 20

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Unformatted text preview: ntervals of length Dt = 3 days. (c) A student proposes the function P, given by P (t ) = 20 + 10 te 0 − t / 35 , as a model for the temperature of the water in the pond at time t, where t is measured in days and P (t ) is measured in degrees Celsius. Find P ′(12). Using appropriate units, explain the meaning of your answer in terms of water temperature. (d) Use the function P defined in part (c) to find the average value, in degrees Celsius, of P (t ) over the time interval 0  t  15 days. Copyright © 2001 by College Entrance Examination Board. All rights reserved. Advanced Placement Program and AP are registered trademarks of the College Entrance Examination Board. GO ON TO THE NEXT PAGE. 3 2001 AP® CALCULUS AB FREE-RESPONSE QUESTIONS 3. A car is traveling on a straight road with velocity 55 ft/sec at time t = 0. For 0  t  18 seconds, the car’s acceleration a t , in ft/sec2 , is the piecewise linear function defined by the graph above. 05 (a) Is the velocity of the car increasing at t = 2 seconds? Why or why not? (b) At what time in the interval 0 ≤ t ≤ 18, other than t = 0, is the velocity of the car 55 ft/sec? Why? (c) On the time interval 0 ≤ t ≤ 18, what is the car’s absolute...
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