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In a court case a judge cited a city for contempt and

Question: In a 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, $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)?

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