Find function type from list of points

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I have a list of points, and plotting them on a graph it looks like a Log/esponential graph.. But none of the generic formulas give me a function that returns all the points. ($y=a*b^x+k$, $y=log b(x-a)$)

How can I, strating from the given points, find the function?

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Edit:

The values are in mm, and are a measurement. In reallife the x values go from 0 to 800. So an aproximation that returns values within a tollerance of +/-3mm in the range from 0 to 800 is good enough. The Y values are the values for this specific machine. In real life each machine will have different Y values, and I will also have only 3 points. (for example 0,300,600) What I would need is a way to find a function with 3 given points.