Finding a Power Function for a Set of Data: Techniques and Tips

[lalala_land89]

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 don't even know where to start or how.
x y
32 6
48 14
64 24
80 38
96 55
112 75
OK may be I am stupid but I'm in calc and yes i don't know how to come with a function. so please help.
marina

 

[Gib Z]

$$y=(1.9\cdot 10^{-5})x^3 + 0.004x^2 + 0.052x - 0.0622$$
$$y = (1.1\cdot 10^{-7})x^4 + (2.2\cdot10^-5)x^3 + 0.0019x^2 + 0.208x - 3.28$$
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 a lot. 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.

 

[AlephZero]

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.

 

[lalala_land89]

i can't use technology for this i have to derive it myself.

 

[lalala_land89]

im not aware of that method i'll try it. does anyone else have any ideas?

 

[Hurkyl]

Please don't post the same question multiple times.

 

[lalala_land89]

i didnt post twice. i posted in math forum first not realizing there's a homework forum. I'm new here. i don't quiete get the method you told me about. anymore ideas?