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Modeling with power functions

Modeling with power functions.

I have turned to every book i own on math from algebra to math encyclopedia to calculus ab book. I seriously don't know how to come up with a power function for a set of data. I don't even know any techniques. There are no zeros or intercepts to this set of data.if anyone could please help me come with this function. i dont even know where to start or how.
x y
32 6
48 14
64 24
80 38
96 55
112 75
OK may be im stupid but i'm in calc and yes i dont know how to come with a function. so please help.

Answers and Replies

Gib Z
Homework Helper
[tex]y=(1.9\cdot 10^{-5})x^3 + 0.004x^2 + 0.052x - 0.0622[/tex]
[tex]y = (1.1\cdot 10^{-7})x^4 + (2.2\cdot10^-5)x^3 + 0.0019x^2 + 0.208x - 3.28[/tex]
They both fit pretty well, but the 2nd one fits better i think.

You know how to find the derivative at a point yes? Look up Taylor series on wikipedia and on this forum, it'll help alot. FYI i didnt get that approximation through that Method, I used my computer. More data points will get a more accurate curve, post more data if you want.
Last edited:
Science Advisor
Homework Helper
The usual way to fit a power function y = Ax^b is to take logs and fit the straight line (log y) = (log A) + b (log x)

A search for "Least squares method" should find more details.
i cant use technology for this i have to derive it myself.
im not aware of that method i'll try it. does anyone else have any ideas?
Staff Emeritus
Science Advisor
Gold Member
Please don't post the same question multiple times.
i didnt post twice. i posted in math forum first not realizing there's a homework forum. i'm new here. i dont quiete get the method you told me about. anymore ideas?