AP Calculus AB and BC 2014 Question 1 and Answers

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Questions and Worked Solutions for AP Calculus AB and BC 2014.

AP Calculus AB 2014 Free Response Questions - Complete Paper (pdf)

AP Calculus BC 2014 Free Response Questions - Complete Paper (pdf)

AP Calculus AB and BC 2014 Free Response Question 1
A graphing calculator is required for these problems.

1. Grass clippings are placed in a bin, where they decompose. For 0 ≤ t ≤ 30, the amount of glass clippings remaining in the bin is modeled by A(t) = 6.687(0.931)^t, where A(t) is measured on pounds and t is measured in days.
(a) Find the average rate of change A(t) over the interval 0 ≤ t ≤ 30. Indicate units of measure.
(b) Find the value of A'(15). Using correct units, interpret the meaning of the value in the context of the problem.
(c) Find the time t for which the amount of grass clipping in the bin is equal to the average amount of grass clipping in the bin over the interval 0 ≤ t ≤ 30.
(d) For t > 30, L(t), the linear approximation to A at t = 30, is a better model for the amount of grass clippings remaining in the bin. Use L(t) to predict the time at which there will be 0.5 pound of grass clippings remaining in the bin. Show the work that leads to your answer.

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