(a) Explanation Given: A logistic growth model is: d P d t = k P ( C − P ) with k = 0.007 And the carrying capacity: C = 10 million Let t = 0 correspond to the year 1980 when seal population was estimated to be about 2 million. Calculation: Consider the Logistic growth model and put the value of carrying capacity C and Proportionality factor k . d P d t = 0.007 P ( 10 − P ) 1 P ( 10 − P ) d P = 0.007 d t Now, integrate both sides of above equation. ∫ 1 P ( 10 − P ) d P = ∫ 0.007 d t The right side of the above equation can be integrated but left side does not match any standard form of integration formulae. Now, use the following identity with C = 10 to integrate left side, 1 P ( C − P ) = ( 1 C ) P + ( 1 C ) C − P Then, ∫ ( 1 10 ) P + ( 1 10 ) 10 − P = 0.007 t + k 1 10 ln ( P ) − 1 10 ln ( 10 − P ) = 0.007 t + k 1 10 ln ( P ) − 1 10 ln ( 10 − P ) = .007 t + k 0.1 ln ( P ) − 0.1 ln ( 10 − P ) = .007 t + k Further simplification, ln ( P ) 0.1 − ln ( 10 − P ) 0.1 = .007 t + k ln ( P 10 − P ) 0.1 = 0.007 t + k Now, take exponent of both sides (b) To determine To calculate: The seal population in the year 2012 and year 2018 . (c) To determine The year when seal population reaches 8 million .

MyLab Math with Pearson eText -- Standalone Access Card -- for Mathematics with Applications in the Management, Natural, and Social Sciences (12th Edition)

12th Edition

ISBN: 9780134856551

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

Publisher: PEARSON

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Chapter 13, Problem 3CE

(a)

To determine

To calculate: A Population function by use of logistic growth model.

(b)

To determine

To calculate: The seal population in the year 2012 and year 2018.

(c)

To determine

The year when seal population reaches 8 million.

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Chapter 13, Problem 2CE

Chapter 13, Problem 4CE

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MyLab Math with Pearson eText -- Standalone Access Card -- for Mathematics with Applications in the Management, Natural, and Social Sciences (12th Edition)

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