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Modeling with power functions

  1. Dec 27, 2006 #1

    lalala_land89

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    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
     
    lalala_land89, Dec 27, 2006
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  3. Dec 28, 2006 #2

    Gib Z

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    [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: Dec 28, 2006
    Gib Z, Dec 28, 2006
  4. Dec 28, 2006 #3

    AlephZero

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    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.
     
    AlephZero, Dec 28, 2006
  5. Dec 28, 2006 #4

    lalala_land89

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    i cant use technology for this i have to derive it myself.
     
    lalala_land89, Dec 28, 2006
  6. Dec 28, 2006 #5

    lalala_land89

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    im not aware of that method i'll try it. does anyone else have any ideas?
     
    lalala_land89, Dec 28, 2006
  7. Dec 28, 2006 #6

    Hurkyl

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    Please don't post the same question multiple times.
     
    Hurkyl, Dec 28, 2006
  8. Dec 28, 2006 #7

    lalala_land89

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    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?
     
    lalala_land89, Dec 28, 2006
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