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# Natural Logs and Exponential Decay Help! Watch

1. 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.
2. (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:

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.

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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Updated: March 27, 2013
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