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ts. For what initial values P(0) = P0 does this model

A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill ISBN: 9781111827052 44

Solution for problem 39E Chapter 2.1

A First Course in Differential Equations with Modeling Applications | 10th Edition

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A First Course in Differential Equations with Modeling Applications | 10th Edition | ISBN: 9781111827052 | Authors: Dennis G. Zill

A First Course in Differential Equations with Modeling Applications | 10th Edition

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Problem 39E

PROBLEM 39E

Population Model Another population model is given by

where h and k are positive constants. For what initial values P(0) = P0 does this model predict that the population will go extinct?

Step-by-Step Solution:
Step 1 of 3

Solution:-

Step1

Given that

We have to find that for what initial values P(0) =  does this model predict that the population will go extinct?

Step2

We have

Population model

-----------------------(1)

where h and k are positive constants.

The equation is first order linear differential equation.

By using integrating factor

Step3

Solution for equation (1) is given by

          =

Where C is integration constant.

From (2) we get

P(t)=

Step4

When P(0)=

Put  in (3) we get

If

This shows that  is the equilibrium solution.

Step5

This means the population will go extinct,

Therefore, the population becomes extinct when,

Step 2 of 3

Chapter 2.1, Problem 39E is Solved
Step 3 of 3

Textbook: A First Course in Differential Equations with Modeling Applications
Edition: 10
Author: Dennis G. Zill
ISBN: 9781111827052

This full solution covers the following key subjects: model, population, another, given, initial. This expansive textbook survival guide covers 109 chapters, and 4053 solutions. The full step-by-step solution to problem: 39E from chapter: 2.1 was answered by , our top Calculus solution expert on 07/17/17, 09:41AM. A First Course in Differential Equations with Modeling Applications was written by and is associated to the ISBN: 9781111827052. The answer to “Population Model Another population model is given by where h and k are positive constants. For what initial values P(0) = P0 does this model predict that the population will go extinct?” is broken down into a number of easy to follow steps, and 32 words. This textbook survival guide was created for the textbook: A First Course in Differential Equations with Modeling Applications, edition: 10. Since the solution to 39E from 2.1 chapter was answered, more than 648 students have viewed the full step-by-step answer.

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ts. For what initial values P(0) = P0 does this model