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 (that is, the fine progressed as follows:

$2, $4, $16, $256, $65, 536, . . .).

a. What would be the fine on day N?

b. How many days would it take the fine to reach D dollars? (A Big-Oh answer will do.)