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Math Help - Word problem - law of uninhibited growth

  1. #1
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    Word problem - law of uninhibited growth - please help me finish! :)

    A culture of bacteria obeys the law of uninhibited growth. N(t) = N0(e)^kt

    If 500 bacteria are initially present and there are 80 after 1 hour, how many will be present after 5 hours? How long is it until there are 20,000 bacteria?

    So, 800 = 500e^k and 800 = 1359.14^k

    I cant get past this, how do I get the rate, divide each side by 1359.14?? Once I have the rate I can get the rest, correct?
    Last edited by rtwilton; November 25th 2008 at 06:08 AM.
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  2. #2
    Member Henderson's Avatar
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    Careful- you can't multiply 800 by e before you take care of your exponent.

    Your best bet at this point:

    800 = 500e^k

    \frac{800}{500} = \frac{500e^k}{500}

    1.6 = e^k

    ln(1.6) = k
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  3. #3
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    Thank you!! So to answer the question how many bacteria will there be in 5 hours...

    N(5) = 500e^ln(1.6)(5)

    Hmmm this doesn't seem to work...


    And for the other part of the question would it be

    20,000 = 500e^ln(1.6)(5)

    ??
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