The Houston, Texas area has experienced "exponential growth." What does that mean? How can we check?
The population of the world is growing at an alarming rate. What will the population be in five years? ten years?
In 1840 a Belgian mathematician predicted what the population of the United States would be in 1940 -- one hundred years later. His prediction was off by less than 1%. How did he do it? And how is this connected to the study of the Maine lobster population?
We will address all of these questions by examining three differential equation models of population growth -- the natural growth or exponential growth model, the coalition model for world population growth, and the logistic growth model. In each case we will examine the model, discuss ways of checking to see if it is appropriate for a given set of data, and construct models to fit one or more sets of data.
Throughout we will assume familiarity with the notion of a first-order initial value problem as a mathematical model for a set of data. The module Introduction to Differential Equations provides a quick introduction to (or review of) this notion. This introductory module also contains a discussion of slope fields and the symbolic solution of separable first-order differential equations -- both of which we will need in the present module.
