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Math Help - Need to solve an equation for a constant value.

  1. #1
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    Need to solve an equation for a constant value.

    dL/dt = k(1-L)

    This is a logistic function, if I'm not mistaken.

    It's a lab in my DE book. I need to find my personal k value. It's about rate of memorization.

    It says I can use numerical methods or analytic methods. The problem is I don't know how to do either, apparently. I have my data, I just don't know how to apply it.

    Any help?
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  2. #2
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    Quote Originally Posted by pantsaregood View Post
    dL/dt = k(1-L)

    This is a logistic function, if I'm not mistaken.

    It's a lab in my DE book. I need to find my personal k value. It's about rate of memorization.

    It says I can use numerical methods or analytic methods. The problem is I don't know how to do either, apparently. I have my data, I just don't know how to apply it.

    Any help?
    Can you not separate the variables?

    \frac{dL}{1-L} = k \, dt
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  3. #3
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    Yes.

    It comes out to

    L = e^kt + 1

    I don't really see how this allows me to solve for k, since I have several L and t values. Those values all require k to be something different.

    ln(L-1)/t = k

    I have ten different values for L and t. How do I work with that?
    Last edited by pantsaregood; March 7th 2010 at 11:17 AM.
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  4. #4
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    Quote Originally Posted by pantsaregood View Post
    Yes.

    It comes out to

    L = e^kt + 1

    I don't really see how this allows me to solve for k, since I have several L and t values. Those values all require k to be something different.

    ln(L-1)/t = k

    I have ten different values for L and t. How do I work with that?
    I have as solution of the DE [imath]L(t)=1-A\cdot e^{-k\cdot t}[/imath] Now you have two unknown parameters "A" and "k" which you can find by applying the least squares method on your data with this equation.

    Coomast
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