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Math Help - Finding function from a graph

  1. #1
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    Finding function from a graph

    I need to find a function from these numbers:

    Finding function from a graph-finding.jpg

    How could I do that?
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  2. #2
    A Plied Mathematician
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    Do you have an underlying model for the data? Or do you not have any clues as to the type of function the data is supposed to represent?
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  3. #3
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    All I know about this is that this is humidity on the x axis and resistance in k ohms on the y axis. These numbers are almost linear on a semi log (if i'm not mistaken thats how it is called) scale.
    Attached Thumbnails Attached Thumbnails Finding function from a graph-findings2.jpg  
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  4. #4
    A Plied Mathematician
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    Ah. That doesn't surprise me in the least. And yes, that is a semilog plot. Probably the easiest thing to do is to fit a straight line to the semilog plot of your data. The idea is this: assume your function (on the original plot) is of the form

    y=A\,e^{-k t}.

    Here it is essential that both A>0 and k>0.

    Now, plotting in a semilog plot is the same as taking the logarithm of both sides of this equation. The result is the following:

    \ln(y)=\ln(A)+\ln(e^{-kt})=\ln(A)-kt.

    Your semilog plot has essentially plotted \ln(y) versus t. Therefore, you can find the slope and intercept of a straight-line-fit. The slope will be -k, and the intercept \ln(A).

    Make sense?
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  5. #5
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    Thank you. Solved my problem. The graph itself seems to be not a perfect exponent, because my solution does not correspont to the given graph perfectly. But thats not a problem in this case.

    Thank you again.
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  6. #6
    A Plied Mathematician
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    You're welcome. Have a good one!
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