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:

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 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.