Modeling Growth of E. Coli Bacteria
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
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.
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.
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