## 2015 Message to Garcia

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)

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)