Introduction

Differential Equations and Population Growth

The size of a population at any given time depends upon the rate at which the population is growing. The rate at which a population grows changes with time, therfore, the population does not always grow by the same amount over equal intervals of time. It is the goal of this lesson to solve population problems for populations that grow at a changing rate.

Purpose

To solve population problems in which the population grows at a rate thea is directly proportional to the number of members present in the population

Objectives

For a population that grows at a rate that is directly proportional to the number of members present in the population:

1. calculate the size of the population at a given time,

2. calculate the time at which the population will be a given size.

Overview of Content

1. A discussion of what a differential equation is and how it relates to a particular population problem.

2. Solving a particular differential equation to get the function that will be used to satisfy the objectives.

3. Example problems.

4. Closure.

5. A quiz over the lesson.

Materials Needed

1. Paper

2. Pencil

3. A scientific calculator that has the natural logratigm and natural exponential frnctions.

Time

Fifty minutes and up.

Prior Knowledge

1. Algebra.

2. How to differentiate functions including the natural logarithm and natural exponential functions.

3. How to integrate functions including the natural logarithm and natural exponential functions.

4. Properties of the natural logarithm and natural exponential functions.

5. How to calculate the values of the natural logarithm function and natural exponential function on a calculator.

T

These
pages were made through TeacherTECH,

the teacher professional development component of GirlTECH, which is sponsored

by the Center for Excellence and Equity in Education (CEEE) with support from

the National Science Foundation through EOT-PACI.

Copyright @ June 2001 by Charles Pate.

the teacher professional development component of GirlTECH, which is sponsored

by the Center for Excellence and Equity in Education (CEEE) with support from

the National Science Foundation through EOT-PACI.

Copyright @ June 2001 by Charles Pate.