Exponential decay/growth

  • Thread starter h00zah
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  • #1
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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
 

Answers and Replies

  • #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.
 
  • #3
fzero
Science Advisor
Homework Helper
Gold Member
3,119
289
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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