Distinguishing the difference between root graphs

[fred2028]

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 ...

Now to clarify. I know that y=1/x^3 is a lot steeper than y=1/x^2, but one can transform y=1/x^2 to make it steeper ...

 

[Deleted member 4993]

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 ...

Now to clarify. I know that y=1/x^3 is a lot steeper than y=1/x^2, but one can transform y=1/x^2 to make it steeper ...

There are numerical methods - which can do the job you are asking for. Have you taken any course in numerical analysis? In the absence of that, graphing is the only other route.

You cannot make 1/x^2 look like 1/x^3 - by simple transformation of graphs such as shift (add/subtract constant) or expansion/contraction (multiply/divide by constant) or by rotation (matrix multiplication).