In A Recent Court Case A Judge Cited A City

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.)

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