Modeling with power functions

1. Dec 27, 2006

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 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.
marina

2. Dec 28, 2006

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 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: Dec 28, 2006
3. Dec 28, 2006

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.

4. Dec 28, 2006

lalala_land89

i cant use technology for this i have to derive it myself.

5. Dec 28, 2006

lalala_land89

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

6. Dec 28, 2006

Hurkyl

Staff Emeritus
Please don't post the same question multiple times.

7. Dec 28, 2006

lalala_land89

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?