Problem

Suppose we want to model the growth of a bacteria colony. We know that the rate of change of the population (P) is directly proportional to the population. Early observations suggest that they are in fact equal. If the initial population is 100, use Euler's method with stepsize = 0.1 to predict the population in 6 hours.

Solution

The differential equation we are concerned with is

an in our case, observations say k = 1, so

The initial condition is t = 0, P = 100. The Euler's method applet on the Web page comes up with P approximately equal to 30448 when t equals 6.