Suppose that r(t) = r 0 e -kt , with k > 0, is the rate at

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Suppose that r(t) = r0 e-kt, with k > 0, is the rate at which a nation extracts oil, where r0 = 107 barrels/yr is the current rate of extraction. Suppose also that the estimate of the total oil reserve is 2 × 109 barrels. 

a. Find Q(t), the total amount of oil extracted by the nation after t years.

b. Evaluatelim Q(t) t- and explain the meaning of this limit.

c. Find the minimum decay constant k for which the total oil reserves will last forever.

d. Suppose r0 = 2 × 107 barrels/yr and the decay constant k is the minimum value found in part (c). How long will the total oil reserves last?

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Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

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