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. Evaluateand 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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Related Book For answer-question

Calculus Early Transcendentals

ISBN: 978-0321947345

2nd edition

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

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Question Posted: Apr 12, 2019 10:22 AM

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

Question:

lim Q(t) t-

Step by Step Answer:

a Qt f rt dt f 107ekt dt 10ekt C When t 0 we have Q0 0 so C 10 0 so 1071ekt C 107 Thus Qt k 1...View the full answer

Calculus Early Transcendentals

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