(a) 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.

Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

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ISBN: 9780134996103

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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Single Variable Calculus: Early Transcendentals, Books a la Carte, and MyLab Math with Pearson eText -- Title-Specific Access Card Package (3rd Edition)

Ch. 7.1 - What is the domain of ln |x|?Ch. 7.1 - Quick Check 2 Simplify e ln 2x, ln (e2x), e2 ln x,...Ch. 7.1 - Prob. 3QC Ch. 7.1 - Prob. 4QC Ch. 7.1 - Prob. 1E Ch. 7.1 - Prob. 2E Ch. 7.1 - Evaluate 4xdx.Ch. 7.1 - Prob. 4E Ch. 7.1 - Express 3x, x, and xsin x using the base e.Ch. 7.1 - Prob. 6E

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

Solution Summary: The author calculates the amount of oil consumed over the year from the beginning of the course. The exponential growth is characterized by a constant relative growth rate.

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

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

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

Want to see the full answer?

Chapter 7 Solutions