(a) Explanation Given: The growth rate of the population is f ( t ) = 66 t ( 17 ≤ t ≤ 47 ) Here, t = 17 corresponds to the year 2017. Formula used: The integration of function f ( x ) = k x is performed as, I = ∫ k x d x = k ln ( x ) + c Here, k is a constant and c is the integration constant. Calculation: The derivative of the population function F ( t ) is the rate at which population is growing. This means that the function for growth rate of the population f ( t ) , is the derivative of F ( t ) . F ( t ) = ∫ f ( t ) d t Substitute 66 t for f ( t ) (b) To determine The value of F ( 47 ) and interpret its significance.

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

12th Edition

ISBN: 9780134767628

Author: Margaret L. Lial, Thomas W. Hungerford, John P. Holcomb, Bernadette Mullins

Publisher: PEARSON

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Chapter 13.1, Problem 57E

(a)

To determine

To calculate: The function F(t) which gives the projected population in year t, if the population of the united states was about 326 million in the year 2017.

(b)

To determine

The value of F(47) and interpret its significance.

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Chapter 13.1, Problem 56E

Chapter 13.1, Problem 58E

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Chapter 13 Solutions

Mathematics with Applications In the Management, Natural, and Social Sciences (12th Edition)

Ch. 13.1 - Checkpoint 1 Find an antiderivative for each of...Ch. 13.1 - Checkpoint 2 Find each of the...Ch. 13.1 - Prob. 3CP Ch. 13.1 - Prob. 4CP Ch. 13.1 - Prob. 5CP Ch. 13.1 - Prob. 6CP Ch. 13.1 - Prob. 7CP Ch. 13.1 - Checkpoint 8 The marginal cost at a level of...Ch. 13.1 - 1. What must be true of F(x) and G(x) if both are...Ch. 13.1 - 2. How is the antiderivative of a function related...

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The function F ( t ) which gives the projected population in year t , if the population of the united states was about 326 million in the year 2017.

Solution Summary: The author calculates the function F(t) which gives the projected population in year t, if the population of the united states was about 326 million in the year 2017.