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Help Finishing a Logistic Model

  1. Mar 14, 2008 #1
    I am working on a population model using US population data. I have done a scatter plot, linear regression and now need to complete.

    This is what I have:

    y = .0287 - .0000917x

    (1/P) (dP/dt) = b + aP

    I have set this up to integrate and by keeping the variables a and b in the equation and using partial fractions get:

    ln |P/(b + aP)| = bt + bC

    ln |P/(.0287 - .0000917P)| = .0287t + .0287C

    at t = 0, P0 = 3.9, so C = 1/.0287 ln 137.6

    ln |P/(.0287 - .0000917P)| = .0287t + ln 137.6 the take exponential of each side

    P/|.0287 - .0000917P| = 137.6e^.0287t

    This is where it gets confusing. I pulled a P out of the denominator to get only one P

    P/P|.0287/P - .0000917| = 137.6e^.0287t

    1/|.0287/P - .0000917| = 137e^.0287t

    I think I should swap the denominator on the left with the numerator on the right but not sure if I can do this with "e". Any advice or suggestions would be appreciated. Thanks.
  2. jcsd
  3. Mar 14, 2008 #2


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    Why can't you do that with e?
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