In a recent court case, a judge cited a city for contempt and ordered a fine of $2 for the first day. Each subsequent day, until the city followed the judge's order, the fine was squared (i.e., the fine progressed as follows: $2, $4, $16, $256, $65536, ... ).
a. What would be the fine on day N?
b. How many days would it take for the fine to reach D dollars? (A Big-Oh answer will do.)