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{7502, 6610, 4988, 2861, 2242, 1746, 1433, 1312, 949, 793, 767, 664, 660, 653, 588, 578, 575, 572, 553, 500, 445, 418, 374, 165, 108}

I was looking at the number of seeds for torrent files for episodes of The Office as they get older and, the older an episode is the less seeds there are. I thought maybe the data would look like exponential decay.

What other types of function might I consider for the best fit, or do you think this is the most appropriate?

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One trick for recognizing a good function when it "seems exponential" is to look at the data in a log scale (take the logarithm of the data). If it is exponential it will look like a straight line. – Bitwise Oct 7 '12 at 3:54
What do these values represent? How do we get the plot by J.G. from them? – marty cohen Oct 7 '12 at 4:11
It looks decidedly not like a straight line in a log plot: – Rahul Oct 7 '12 at 5:13
@Bitwise That's good advice. I've actually never used log scales for anything, but now I have a reason. – Korgan Rivera Oct 7 '12 at 16:06

Exponential seems like a good guess. For instance, $y=e^{x/3+7/8}+500$ forms a descent approx. :

enter image description here

(replace $x$ with $-x$ if you want it as decay)

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