# Your work must be expressed in standard mathematical

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Your work must be expressed in standard mathematical notation rather than calculatorsyntax.For example,15x2dxmay not be written as fnInt(X2,X,1,5).Unless otherwise specified,answers(numeric or algebraic)need not be simplified.If youuse decimal approximations in calculations,your work will be scored on accuracy.Unless otherwise specified,your final answers should be accurate to three places afterthe decimal point.Unless otherwise specified,the domain of a functionfis assumed to be the set of allreal numbersxfor whichf xis a real number.AP®Calculus BC ExamSECTION II: Free Response2012Form IForm Code 4IBP-S268Minimum 20% post-consumer waste
Unauthorized copying or reuse of any part of this page is illegal.1111111111Continue problem 1 on page 5. -4- t(minutes) 0 4 9 15 20 ( )W t(degrees Fahrenheit) 55.0 57.1 61.8 67.9 71.0 1. The temperature of water in a tub at time tis modeled by a strictly increasing, twice-differentiable function Wwhere ( )W tis measured in degrees Fahrenheit and tis measured in minutes. At time 0,t=the temperature of the water is 55 F.The water is heated for 30 minutes, beginning at time 0.t=Values of ( )W tat selected times tfor the first 20 minutes are given in the table above. (a) Use the data in the table to estimate ()12 .W¢Show the computations that lead to your answer. Using correct units, interpret the meaning of your answer in the context of this problem. (b) Use the data in the table to evaluate ( )200.Wtdt¢ÚUsing correct units, interpret the meaning of ( )20Do not write beyond this border. Do not write beyond this border. , 0Wtdt¢Úin the context of this problem.
Unauthorized copying or reuse of any part of this page is illegal.1111111111GO ON TO THE NEXT PAGE. -5- (c) For 020,t££the average temperature of the water in the tub is ( )020W tdtÚUse a left Riemann sum with the four subintervals indicated by the data in the table to approximate ( )2001.20W tdtÚDoes this approximation overestimate or underestimate the average temperature of the water over these 20 minutes? Explain your reasoning. (d) For 2025,t££the function Wthat models the water temperature has first derivative given by ( )()0.4cos 0.06.Wttt=¢Based on the model, what is the temperature of the water at time 25 ?Do not write beyond this border. Do not write beyond this border. 201.t=
Unauthorized copying or reuse of any part of this page is illegal.2222222222Continue problem 2 on page 7. -6-