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.
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.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
More videos, activities and worksheets that are suitable for Calculus
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)
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.
Rotate to landscape screen format on a mobile phone or small tablet to use the Mathway widget, a free math problem solver that answers your questions with step-by-step explanations.
You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.
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