This problem requires a calculator. Enter answers as decimals.
Grass clippings are placed in a bin, where they decompose. The amount of grass clippings measured in kilograms is modeled by A(t)=7.0(0.95)t, where t is measured in days.
(a) Find the average rate of change of A(t) over the interval 0≤t≤30, in kilograms per day.
(Enter your answer to two decimal places.)
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(b) Find the value of A′(15).
(Enter your answer to two decimal places.)
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(c) Let L(t) be the linear approximation to A at t=15. Use L(t) to predict the time at which there will be no grass clippings remaining.
(Round to nearest integer.)
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