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
w1 = (100’000 x 7)2
w2 = (100’000 x 7 + w1)2
wn = (100’000 x 7 + wn-1)2
It looks like it’s impossible to find a true function for wn that depens only on n.
But we can approximate it with:
w_n = C^(2^n)
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.
w_n = (4.9 * 10^11)^(2^(n-1))
where n is the number of weeks since the fine was issued.
In truth wn 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.
Initially, the fine wasn’t that large. However, the exponential increase kicks hard.
It’s an interesting formula. Exponential and logarithmic I think?
I’m not a super great at math terms person
14k first week 42k the second 98k the third 210k 434k 882k 1778k…
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
w1 = (100’000 x 7)2
w2 = (100’000 x 7 + w1)2
wn = (100’000 x 7 + wn-1)2
It looks like it’s impossible to find a true function for wn that depens only on n.
But we can approximate it with:
w_n = C^(2^n)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.
w_n = (4.9 * 10^11)^(2^(n-1))where n is the number of weeks since the fine was issued.
In truth wn 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.