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Math Help - Population growth

  1. #1
    Newbie
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    Oct 2009
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    Population growth

    Here is my problem:

    "A bacteria culture grows with the constant relative growth rate. After 2 hours there are 600 bacteria and after 800 hours the count is 75,000.

    Find the initial population."

    I know I need to use P(t)=P(0)(e^kt) but can't figure out how to solve for P(0). I'm sure it is probably obvious, but I am stumped. Any help is appreciated.
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  2. #2
    MHF Contributor
    Joined
    Mar 2007
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    Talking

    You are given two data points, (t, P) = (2, 600) and (t, P) = (800, 75000). Plug these values in, and solve the resulting system of equations for the values of P0 and k.
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  3. #3
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    Oct 2009
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    That's what I did first, but I got 0.0060505 for K, which seemed like it couldn't be right. I guess my prof just wanted to give us crappy numbers to work with :/ Thanks.
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