Modeling Growth of E. Coli Bacteria

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
"n of x equals n sub zero time e raised to the  0.014x
Suppose N sub zero= 500,000 is the initial number of bacteria per milliliter.
(Source: G. S.Stent, Molecular Biology of Bacterial Viruses.)

This model will be examined by:

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

b). Determining graphically the elapsed time when there were 25 million bacteria per milliliter.

 

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