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Exponential decay/growth

  1. Oct 29, 2010 #1
    if i have a set of data, where as time increases, so does y, but is bounded by a number say y=c, how do i formulate my equation? how do i find the constants?

    i have y=c-a-x*b

    this is basically a transformation of y=b*ax+c
     
  2. jcsd
  3. Oct 29, 2010 #2

    fzero

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    If you have some reason to believe that

    [tex] y = c - b a^x[/tex]

    is the function that fits the (x,y) data, you can compute

    [tex] \ln (c-y) = (\ln a) x + \ln b.[/tex]

    If you can find c from the asymptotic form of y, then a plot of [tex]\ln (c-y)[/tex] vs x will be linear. You can read [tex]\ln a[/tex] from the slope and [tex]\ln b[/tex] from the intercept. You can read up on linear regression theory if you want to determine the accuracy of the fit.
     
  4. Oct 29, 2010 #3

    fzero

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    If you have some reason to believe that

    [tex] y = c - b a^x[/tex]

    is the function that fits the (x,y) data, you can compute

    [tex] \ln (c-y) = (\ln a) x + \ln b.[/tex]

    If you can find c from the asymptotic form of y, then a plot of [tex]\ln (c-y)[/tex] vs x will be linear. You can read [tex]\ln a[/tex] from the slope and [tex]\ln b[/tex] from the intercept. You can read up on linear regression theory if you want to determine the accuracy of the fit.
     
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