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Math Help - Stuck with finding roots including population models

  1. #1
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    Stuck with finding roots including population models

    Hi,

    I would like to find the solution for t in;

    a*t=1/(1+c*exp(-b*t))

    where a, b and c are all positive and less than 1. Left hand side of the function is cumulative logistics curve. I know it is not invertible, I am assuming the solution would include LambertW function. Is there a way to find t in closed form (using LambertW or any other functions)?
    Thanks,
    rutabaga
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  2. #2
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    Quote Originally Posted by rutabaga View Post
    . . . or any other functions)?
    Thanks,
    rutabaga
    Here's a numerical approach in Mathematica:

    Code:
    f[a_, b_, c_, t_] := a^t - 1/(1 + c/E^(b*t)); 
    g[x_, y_, z_] := t /. FindRoot[f[x, y, z, t] == 0, {t, 0}]
    Last edited by shawsend; August 18th 2008 at 05:54 AM. Reason: removed unnecessary wording
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