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Calculus / A First Course in Differential Equations with Modeling Applications 10 / Chapter 1.3 / Problem 2E

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

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The population model given in (1) fails to take death into

Chapter 1, Problem 2E

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QUESTION:

The population model given in (1) fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the population changes is a net rate—that is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the population present at time t > 0.

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QUESTION:

The population model given in (1) fails to take death into consideration; the growth rate equals the birth rate. In another model of a changing population of a community it is assumed that the rate at which the population changes is a net rate—that is, the difference between the rate of births and the rate of deaths in the community. Determine a model for the population P(t) if both the birth rate and the death rate are proportional to the population present at time t > 0.

ANSWER:

Step 1 of 3

We have to determine a model for the population $P(t)$ .

Given, $net\ rate\ =rate\ of\ births\ -rate\ of\ deaths$ …… (1)

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