How do you find a physics formula from a table of values? I can only do it with Excel ...?

Question

How do you find a physics formula from a table of values? I can only do it with Excel ... Like how can you tell when to use y=1/x^3 instead of y=1/x^2, when the graphs look extremely similar? For example, I will type 2 data tables.
_________
A B
2 100
8 200
50 500
200 1000
--------------

____________
E F
2 90
54 270
16 180
250 450
--------------

The first table is square root while the second is cubed root, but when I graphed them, they looked almost exactly the same ...

Answer 1

When physicists are trying to find dependence that is y=ax^b, they plot the values in log-log format. It means that instead of x they plot log(x) on horizontal axis and instead of y they plot log(y) on vertical. If really y=ax^b, the plot would be straight line with slope equal to b. If it is not the case, they try different scales with log only on x or only on y.

In x and y coordinates square root and cube root really look alike with exception that square root starts slower but at large values grows faster.

Answer 2

If they look the same, then you aren't plooting them on identical axes. I'm not exactly sure what you're asking in this question, but if you display the r^2 value on your graph it will give you a rough estimate of how well the fit of your theory is to your data.

Answer 3

You should be able to tell if the axes are marked or by the level of curvature.