Explanation Given: The value of b is 1.5 . The value of r is 0.71 . Carrying capacity is 89 thousand tons. Approach: The standard logistic model is given by, N = K 1 + b e − r t ... ( 1 ) Here, K is the carrying capacity, b is the constant, r is the growth rate and t is the time. Write the expression for the optimum yield. Optimum yield = K 2 ... ( 2 ) Write the expression to calculate the value of b . b = K N ( 0 ) − 1 ... ( 3 ) Calculation: Substitute 89 for K , 1.5 for b and 0.71 for r in equation ( 1 ) . N = 89 1 + 1.5 e − 0.71 t Substitute 89 for K in equation ( 2 ) . Optimum yield = 89 2 = 44.5 thousand tons Substitute 89 for K and 44.5 thousand tons for N ( 0 ) in equation ( 3 ) To determine (b) To find: The time taken by the population to grow from the optimum yield level to 90 % of carrying capacity if b is 4.8 . To determine (c) To compare: The results of part a and part b.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN: 9781337515610

Author: Crauder

Publisher: Cengage

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Chapter 5.1, Problem 22E

To determine

(a)

To find:

The time taken by the population to grow from the optimum yield level to 90% of carrying capacity if b is 1.5.

To determine

(b)

To find:

The time taken by the population to grow from the optimum yield level to 90% of carrying capacity if b is 4.8.

To determine

(c)

To compare:

The results of part a and part b.

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Chapter 5.1, Problem 21E

Chapter 5.1, Problem 23E

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Chapter 5 Solutions

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

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(a) To find: The time taken by the population to grow from the optimum yield level to 90 % of carrying capacity if b is 1.5 .

Solution Summary: The author explains that it takes approximately 3.09 years for population to grow from optimum yield level to 90% of carrying capacity.

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(a)

To find:

The time taken by the population to grow from the optimum yield level to 90% of carrying capacity if b is 1.5.

(b)

To find:

The time taken by the population to grow from the optimum yield level to 90% of carrying capacity if b is 4.8.

(c)

To compare:

The results of part a and part b.

Want to see the full answer?

Chapter 5 Solutions

(a) To find: The time taken by the population to grow from the optimum yield level to 90 % of carrying capacity if b is 1.5 .

Solution Summary: The author explains that it takes approximately 3.09 years for population to grow from optimum yield level to 90% of carrying capacity.

Concept explainers

Videos

(a) To find: The time taken by the population to grow from the optimum yield level to 90% of carrying capacity if b is 1.5.

(b) To find: The time taken by the population to grow from the optimum yield level to 90% of carrying capacity if b is 4.8.

(c) To compare: The results of part a and part b.

Want to see the full answer?

Chapter 5 Solutions

(a)

To find:

The time taken by the population to grow from the optimum yield level to 90% of carrying capacity if b is 1.5.

(b)

To find:

The time taken by the population to grow from the optimum yield level to 90% of carrying capacity if b is 4.8.

(c)

To compare:

The results of part a and part b.