Finding the function of a graph How do I find the function of this graph? You can ignore the first two values before 20 cm.
 A: Given the quantities displayed in your graph (distance from an object emitting radiation), it may be something of the form
$$f\left(x\right) = \frac{1}{ax^2}$$
In order to find a fitting value for the parameter $a$, you could use an error function (a function that for a parameter $a$ gives you the error from the data in your graph). You can then find the parameter $a$ that makes the error function minimal using either numerical methods or calculus.
Given that it's only one parameter, you may of course also try out a few values and see how close you can get.
A: A good idea in such cases is to make a logarithmic or a double logarithmic plot of your data. If the decay is exponential, you will get points approximately on a straight line when you plot $\log(y)$ against $x$. If the decay follows a power law, you will get approximately a straight line when you plot $\log(y)$ against $\log(x)$.
Here the second alternative seems to work best, which suggests that you can use the model
$$\log(y)=a+b\log(x)$$
This can solved for $y$ and rewritten as
$$y={\rm e}^ax^b$$
The parameters $a$ and $b$ can be estimated by performing linear regression of $v=\log(y)$ against $u=\log(x)$. I used the numbers given in Raymond's answer, with the modification that (after deleting the two first points) the first points are given by $$(x_1,y_1)=(1.5,2.75), \qquad (x_2,y_2)=(2,2.52)$$
Then the method of least squares gave me the estimates
$$\hat a=1.50, \qquad \hat b=-0.83$$
Hence your function may be described by
$$y={\rm e}^{1.50}x^{-0.83}=4.48 x^{-0.83}$$
When choosing which model you will use, you have to balance goodness of fit with your theoretic knowledge of the underlying process. There might for instance be physical reasons to prefer (or reject) a power law when modeling reflection properties, even if other models might give better (or worse) fit to the data.
