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2015 Message to Garcia

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2013 AB Calculus Exam

Hot water is dripping through a coffeemaker, filling a large cup with coffee. The amount of coffee in the cup at time t,  0 ≤ t ≤ 6. (Zero is less than or equal to t is less than or equal to six)  is given by a differentiable function C, where t is measured in minutes.

1. Is there a time t, 2≤ t ≤ 4, (two is less than or equal to t is less than or equal to four) at which C'(t) = 2 (C prime of t equals 2)?  Justify your answer.

2. The amount of coffee in the cup, in ounces, is modeled by B(t)= 16 – 16e-0.4t.  (B of t equals sixteen minus sixteen e to the negative zero point four t power).  Using this model, find the rate at which the amount of coffee in the cup is changing when t equals 5.

Selected by Sam Schnur and Andrea Osborne (alias Mrs. Greenwood)


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