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I have few (x,y) raw data and I created a scatter plot with Excel. I'd like to know the actual function that generated this data. I know that there's no method that can automatically find the function, and I know I can find a polinomal expression to approssimate the function. I don't want either of this. I'd like to know if someone can help me out finding a function that fit this graphic and this raw data:

Graph Data

As you see the function is always positive and it's decreasing. I'm thinking about something like

$ e^{-x/k} $

But it doesn't fit perfecly. Thanks for the help.

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    $\begingroup$ Things won't fit perfectly. Look up regression. $\endgroup$ – Sean Roberson Aug 23 '17 at 19:33
  • $\begingroup$ Take logs of the $y$ column & do linear regression on $x$ and $\ln y$. $\endgroup$ – Donald Splutterwit Aug 23 '17 at 19:34
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    $\begingroup$ Yes I know, but I'm 100% sure these values are generated by a script that uses just a single simple function, I need to discover which function is. I don't want to use regression. Think about this as a reverse engineering $\endgroup$ – Giammarco Boscaro Aug 23 '17 at 19:34
  • $\begingroup$ At the very least you'll need to try $Ce^{-x/k}$, since your $y$-intercept is not $1$. You can plug in two data points to try and solve for $k$, and then work back to get $C$. $\endgroup$ – Austin Mohr Aug 23 '17 at 19:40
  • $\begingroup$ Even if you know the right function to use, you would still have to fit a regression to estimate the parameters anyway. If you just want a curve that goes through all the points, you can just fit a polynomial of degree 8 for your 9 data points. $\endgroup$ – Jirapat Samranvedhya Aug 23 '17 at 19:41

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