(a) Explanation Given: The logistic growth rate model is d P d t = k P ( C − P ) . Where, k = 0 , C = 50 and P ( 0 ) = 20 . Formula used: Formula for differentiation is: ∫ 1 x d x = ln x + C Calculation: Consider, the logistic growth rate model is d P d t = k P ( C − P ) . Where, k = 0 , C = 50 and P ( 0 ) = 20 . Integrate the equation d P d t = k P ( C − P ) : ∫ d P P ( C − P ) = ∫ k d t ∫ d P P ( 50 − P ) = ∫ 0.065 d t ∫ d P 50 P + ∫ d P 50 ( 50 − P ) = 0.065 ∫ d t 1 50 ln P − 1 50 ln ( 50 − P ) = 0.065 t + K On solving further, ln P − ln ( 50 − P ) = 3.25 t + 50 K ln P ( 50 − P ) = 3.25 t + 50 K P 50 − P = e 3.25 t + 50 K P = 50 e 3.25 t e 50 K − P e 3 (b) To determine To calculate: The percentage of women participated in 2000, 2016 and 2020 when the function is P ( t ) = 50 e 0.065 t e 0.065 t + 1.5 .

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, Problem 4CE

(a)

To determine

To calculate: The function for percentage of women in Olympic games in year t, when t=0 corresponds to the year 1976 when the logistic growth rate model is dPdt=kP(C−P).

(b)

To determine

To calculate: The percentage of women participated in 2000, 2016 and 2020 when the function is P(t)=50e0.065te0.065t+1.5.

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Chapter 13, Problem 3CE

Chapter 14.1, Problem 1CP

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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 for percentage of women in Olympic games in year t , when t = 0 corresponds to the year 1976 when the logistic growth rate model is d P d t = k P ( C − P ) .

Solution Summary: The author calculates the function for percentage of women in Olympic games in year t, where k=0, C=50 and P(0)=20.