The Problem

The problem: A type of bacteria that inhabits the intestines of animals is named E. coli (Eschenchia coli). These bacteria are capable of rapid growth and can be dangerous to humans -- especially children. In one study, E. coli bacteria were capable of doubling in number every 49.5 minutes. Their number N after x minutes could be modeled by Suppose = 500,000 in the initial number of bacteria per milliliter. (Source: G. S.Stent, Molecular Biology of Bacterial Viruses.)

a). Make a conjecture about the number of bacteria per milliliter after 99 minutes. Verify your conjecture

Solution to part a:

a). Since the number of bacteria double every 49.5 minutes, in 49.5 minutes there would be approximately 1,000,000 bacteria present. (500,000 X 2). So in 99 minutes (2 X 49.5) the number doubles again; thus, there are approximately 2,000,000 bacteria present per milliliter.

To verify this result, substitute 99 for x in the given equation.

So , which gives approximately 2,000,000. To enter this expression into the calculator, press 500000, then 2nd, then the ln key, then 0.014 times 99 and close the parentheses. Next press ENTER.