Read about Thomas Malthus, for whom the Malthusian Model is named.
The simplest model of population growth assumes essentially that the adult (female) members of a population reproduce at a steady rate, usually as fast as they can. This implies that births increase the population at a rate proportional to the population. Similarly, a certain proportion of the population dies off every year -- so deaths decrease the population at a rate proportional to the population. If the proportionality constant for the birth rate is greater than that for the death rate, then the population increases, otherwise it decreases. In this simple situation, the population either increases or decreases exponentially.
In this project, we examine the exponential growth of a population of fast-breeding organisms -- cockroaches. Before moving on to the problems below, view the movie clip that illustrates the situation. [This clip was found to be inoperable on 3/20/2012. The link was removed. Ed.]
Cockroaches are pretty large bugs that breed very quickly. For the purposes of this project, we will assume the following:
Assume that you start with a population of 1 cockroach (don't ask how it reproduces). Then the cockroach population is 2t, where t is measured in minutes.