(a) To determine To find: The amount of oil consumed over the year from the beginning of the course. Explanation Given: The initial rate of consumption of oil is 1.2 million barrels/yr and it increases at a rate of 1.5%/yr. Definition used: Exponential growth function: “Exponential growth is described by functions of the form y ( t ) = y 0 e k t . The initial value of y at t = 0 is y ( 0 ) = y 0 and the rate constant k > 0 determines the rate of growth and the exponential growth is characterized by a constant relative growth rate. Calculation: Consider that the initial rate of consumption of oil is y ( 0 ) = 1.2 million barrels per year. Assume for the first year, the consumption becomes y ( 1 ) = y ( 0 ) + 1.5 % of y ( 0 ) . y ( 0 ) + 1.5 % of y ( 0 ) = y ( 0 ) + 1.5 100 × y ( 0 ) = y ( 0 ) + 0.015 y ( 0 ) = y ( 0 ) ( 1 + 0.015 ) = 1.015 y ( 0 ) Assume for the second year, the consumption becomes y ( 2 ) = 1.015 y ( 0 ) + 1.5 % of 1 .015 y ( 0 ) . That is, 1.015 y ( 0 ) + 1.5 % of 1 .015 y ( 0 ) = 1.015 y ( 0 ) + 1.5 100 × 1 .015 y ( 0 ) = 1.015 y ( 0 ) + ( 0.015 ) 1 .015 y ( 0 ) = 1 .015 y ( 0 ) ( 1 + 0.015 ) = ( 1.015 ) 2 y ( 0 ) Similarly, for the third year, the consumption will be ( 1.015 ) 3 y ( 0 ) . Hence, the general equation for consumption with y ( 0 ) = 1.2 is y ( t ) = 1 (b) To determine To find: The function that provides the total amount of oil used in the interval ( 0 , t ] . (c) To determine The number of years by which the amount of oil would have reached 10 million barrels.

Calculus: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134763644

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

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Chapter 7.2, Problem 26E

(a)

To determine

To find: The amount of oil consumed over the year from the beginning of the course.

(b)

To determine

To find: The function that provides the total amount of oil used in the interval (0,t].

(c)

To determine

The number of years by which the amount of oil would have reached 10 million barrels.

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Chapter 7.2, Problem 25E

Chapter 7.2, Problem 27E

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