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Creating a function based on data using integration

  1. Aug 5, 2009 #1
    1. The problem statement, all variables and given/known data
    I first posted this in the pre-calculus section, then the guy who first came up with the formula hinted at integration, so I guess it's meant to be in the calculus section

    Now this isn't a homework question, it's something me and some others are looking into, and someone posted this function, and I'm not sure how he worked it out:

    So what he's done is used the figures from the albums certified to create an equation. So therefore if you substitute 1 for x in the function, which is actually equal to 500,000 you will get all the albums that certified for over 500,000 sales, it's not exact, but it's a close enough function, how did he work that function out?


    2. Relevant equations
    None


    3. The attempt at a solution

    I have no idea!
     
  2. jcsd
  3. Aug 5, 2009 #2

    Dick

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    Probably just drew a graph and concentrated on the points that seemed to fit a smooth curve. Adjusted a and b in f(x)=1/(ax+b) to fit it. You can use least squares type techniques to help to you estimate the constants. But I'm confused. I put x=1 into 1/(1.23*x+0.278) and I get 0.663. That's not 67. Do you mean I should multiply by 100 also?
     
  4. Aug 5, 2009 #3
    Yea you have to multiply by 100, I got 66.3 too, but I guess he rounded up, not sure why he rounded up, but the other values seems to indicate that's what he did.
     
  5. Aug 5, 2009 #4

    Dick

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    Like I said, you can use least squares to fit almost any smooth curve pretty well. Especially if you start throwing out points that don't fit. And use creative rounding to boot.
     
  6. Aug 5, 2009 #5
    I'm not too sure what that is, but I'll look at it now!

    Thanks Dick.
     
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