Differentiable Function. If a differentiable function f(x) satisfiesf(-4) = f(4)then there exists a c in (-4,4) withO f'(c) > 0O f'(c) < 0O f"(c) = 0O f"(c) > 0O f"(c) < 0O f'(c) = 0O f(c) > 0O f(c) = 0

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Answered: Differentiable Function. If a…

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

ChapterP: Prerequisites

Section: Chapter Questions

Problem 8PS

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Decay of Litter Litter such as leaves falls to the forest floor, where the action of insects and bacteria initiates the decay process. Let A be the amount of litter present, in grams per square meter, as a function of time t in years. If the litter falls at a constant rate of L grams per square meter per year, and if it decays at a constant proportional rate of k per year, then the limiting value of A is R=L/k. For this exercise and the next, we suppose that at time t=0, the forest floor is clear of litter. a. If D is the difference between the limiting value and A, so that D=RA, then D is an exponential function of time. Find the initial value of D in terms of R. b. The yearly decay factor for D is ek. Find a formula for D in term of R and k. Reminder:(ab)c=abc. c. Explain why A=RRekt.
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Differentiable Function. If a differentiable function f(x) satisfies f(-4) = f(4) then there exists a c in (-4,4) with O f'(c) > 0 O f'(c) < 0 O f"(c) = 0 O f"(c) > 0 O f"(c) < 0 O f'(c) = 0 O f(c) > 0 O f(c) = 0