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math 12

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The bacterium Escherichia coli, or
E-coli, has a doubling period of 0.32 h. If a culture starts with 100 bacteria:
(a) Determine the equation for the number of bacteria, y, in x hours.
b) How many hours will pass before there are 450 bacteria in the culture?

  • math 12 -

    a) y = 100 * 2^(x/0.32) (intuitively, after 0.32h, it doubles; after .64h, it quadruples, etc)

    b) plug in y = 450, and solve for x
    you should get x = 0.32*log(4.5)/log(2)
    which is about 0.694h

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