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.
They must have been playing cookie clicker to come up with a fine that big
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.
They did the math.
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.