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Let P(t) be the number of individuals in a population at time , measured in years. If

Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden ISBN: 9781305253667 457

Solution for problem 7 Chapter 5.7

Numerical Analysis | 10th Edition

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Numerical Analysis | 10th Edition | ISBN: 9781305253667 | Authors: Richard L. Burden J. Douglas Faires, Annette M. Burden

Numerical Analysis | 10th Edition

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Problem 7

Let P(t) be the number of individuals in a population at time ?, measured in years. If the average birth rate b is constant and the average death rate d is proportional to the size ofthe population (due to overcrowding), then the growth rate of the population is given by the logistic equation dt where = kP{t). Suppose 7(0) = 50, 976, b 2.9 x I0~2 , and A: = L4x 10-7 . Find the population after 5 years.

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Section 1.2: Basic Ideas and Terminology Definition 1.2.1: A differential equation is an equation involving one or more derivatives of an unknown function. To begin our study of differential equation we need some common terminology. If an equation involves the derivative of one variable with respect with another, then the former is called a dependent variable and the later an independent variable. Example 1: d x dx a kx  0 dt2 dt A differential equation involving ordinary derivatives with respect to a single independent variable is called an ordinary differential equation. A differential equation

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Chapter 5.7, Problem 7 is Solved
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Textbook: Numerical Analysis
Edition: 10
Author: Richard L. Burden J. Douglas Faires, Annette M. Burden
ISBN: 9781305253667

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Let P(t) be the number of individuals in a population at time , measured in years. If