this post was submitted on 30 Oct 2024
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And Finally...
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EDIT: I’m stupid and did it with the fine squaring every week instead of doubling and I’m too lazy to recalculate so ignore this
w~1~ = (100’000 x 7)^2^
w~2~ = (100’000 x 7 + w~1~)^2^
w~n~ = (100’000 x 7 + w~n-1~)^2^
It looks like it’s impossible to find a true function for w~n~ that depens only on n.
But we can approximate it with:
where C is the money owed at the end of the first week.
So the approximate formula for how much is owned at the end of the nth week is.
where n is the number of weeks since the fine was issued.
In truth w~n~ will be larger than said number but it’s a decent lower bounds for approximation and it should be accurate to within around a couple percent.
i did this calculation in rubles but you can just replace 100’000 by 1000 if you wish USD.
Shouldn't it be
w_n = 7 c + 2 w_{n-1}Twice the fine from last week plus c=100000 rubles for each of the seven dow. According to Wolfram alpha this refines to
w(n) = 7 c · (2^n - 1)Anyways, it's a funny formula.
you’re completely right just see the edit I made at the top of my comment
Ah. I first didn't really understand the edit, but now I get it.
They did the math.