(a)
To find the carrying capacity of the population.
(a)
Answer to Problem 26E
The carrying capacity is
Explanation of Solution
Given:
The logistic differential equation describes the growth of a population
Calculation:
The logistic differential equation is given by
Therefore, on comparing it from given logistic differential equation it can be observed that the carrying capacity is
(b)
To find the size of the population when it is growing fastest.
(b)
Answer to Problem 26E
The size of population is
Explanation of Solution
Given:
The logistic differential equation describes the growth of a population
Calculation:
The logistic differential equation is given by
Since, the growth rate is maximum when the population reaches half the carrying capacity.
Therefore ,
Hence, the size of population is
(c)
To find the rate at which the population is growing fastest.
(c)
Answer to Problem 26E
The rate at which the population is growing when it is growing fastest is
Explanation of Solution
Given:
The logistic differential equation describes the growth of a population
Calculation:
The logistic differential equation is given by
Since, for fastest growing rate
So,
Therefore, the rate at which the population is growing when it is growing fastest is
Chapter 7 Solutions
Calculus: Graphical, Numerical, Algebraic: Solutions Manual
Additional Math Textbook Solutions
Calculus and Its Applications (11th Edition)
Calculus, Single Variable: Early Transcendentals (3rd Edition)
Precalculus
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
Calculus & Its Applications (14th Edition)
Precalculus Enhanced with Graphing Utilities (7th Edition)
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