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 |
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.
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