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I implemented a linear function for a search algorithm, that boosts a document according to its time since upload. So the newer a document the more likely it will be presented for a given search term. Maximum age that will be boosted is 365 days (MaxDays) to a maximum of 10 points (MaxBoost).

float MaxDays = 365
float MaxBoost = 10
float calculatedBoost = MaxBoost - (daysPassedSinceUpload * (MaxBoost / MaxDays))

But I am not yet satisfied with the results. So I wonder if an exponential function would work better, where the y-axis will be hit at 10 and the x-axis at 365 (see image). enter image description here Unfortunately it's been a few years since I last did any exponential function in school. Can you please help me to figure out a working function? All I know for now is that is has to be somthing like y=0.5x. Obviously different to cross the axis at right spots. Thanks

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    0.5^(dayspassed/halflife) ought to do what you want with halflife ~100 days. But if you do want it to go negative after MaxDays then subtract off 0.5^(MaxDays/halflife). and rescale. Spreadsheets are good for picking and exploring ad hoc functions. Commented Jul 25, 2024 at 10:24

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The issue with exponential functions is they don't have a root (e^-x never reaches 0, 0 is an asymptote) It is still possible though to use an exponential function but that's gonna require a bit of math.

asymptote = -1
t = ln(asymptote/(asymptote-maxAge)) / maxAge
calculatedBoost = (maxBoost - asymptote) * exp(daysPassedSinceUpload*t) + asymptote

https://www.desmos.com/calculator/vedi0blktp

A better solution might be to use a polynomial! This is also WAYYYY easier n is the degree (strength) of the polynomial

n = 3
calculatedBoost = pow(1-daysPassedSinceUpload/maxAge, n) * maxBoost

https://www.desmos.com/calculator/jbnza17ma0

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2 Comments

Thx. You're right, the polynomial is way easier indeed. But now x is not timePassedSinceUpload anymore. It is (365 - timePassedSinceUpload), which I can work with.
that for pointing that out, I'll edit the answer to fix that error. Also x is not (365 - daysPassedSinceUpload) please check the answer for the correct version, I accidentally swapped the signs...

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