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    In an experiment in physics I have got a curve that looks incredibly like an exponential decay curve, I have been told to prove it is an exponential decay curve using natural logorithms, can somebody please explain how to go about this.
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    (Original post by gmseahorse)
    In an experiment in physics I have got a curve that looks incredibly like an exponential decay curve, I have been told to prove it is an exponential decay curve using natural logorithms, can somebody please explain how to go about this.
    Using natural logs? That's a silly way to prove it... Oh well:

    

Z = Z_0e^{-kt}
    That's your bog standard general decay equation. A and k are constants; Z is your dependant variable, Z0 is the initial value before decay begins.

    

ln(Z) = ln(Z_0) - kt
    Taking logs... If you now plot a graph of ln(Z) against t, you will get a straight line.

    So, if you plot a graph of the natural log of you dependant variable on the y-axis and time on the x-axis, it should be a straight line, with a negative gradient.

    A better way to prove it would be to take ratios. The ratios of subsequent readings of Z should be equal (i.e., Z after 0s divided by Z after 10s should be equal to Z after 10s divided by Z after 20s).
 
 
 
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