Question 1096702
Looking at 40 days (which isn't after 40 days but is the boundary).
Penalty A is 1+(10)(40)=$401 million.  The formula is Cost=$1+$10*t, where the dollars are in millions, and t is the number of days after 1 July ANSWER.
For penalty B, look at it in cents first.  
This is the sum (sigma) of 2^t, with t taken from 0 to 40.
The sum of powers of n: are the highest power (6), add 1 to that power (7) and subtract 1 from the result.

{The sum of 1+2+4+8+16+32+64 is 127).  Here, we have an initial amount of 1 cent or 2^0.
Day 1 is 1 or 2^0,  on day 2 the sum is 3 cents (2^2)-1,  day 3, 4+2+1 or 7 cents (2^3-1); day 4, 15 cents (8+4+2+1) or 2^4-1.
On day 40, it will be 2^40-1 cents.
That is 1.1  x 10 ^12 cents.  While getting the exact number of cents is more difficult, in this instance we aren't asked for that but the relative costs.
This is $1.1 x 10^10, or $11 billion.
A formula in dollars is (1/100)(2^t)-1, where t= days, but this uses 1 July and not the days after which is what the question asks for.  So, for t days after the first, it is 2^(t+1)-2 in cents  (2+4+8+16+32+64+...2^40)
Penalty A is a far wiser choice. The company made the WRONG choice.  ANSWER