The powers of a function f: A → A are defined recursively byOn June 1, you win $1 million...

The powers of a function f: A → A are defined recursively by

On June 1, you win $1 million in a lottery and immediately acquire numerous “friends,” one of whom offers you the deal of a lifetime. In return for the million, she’ll pay you a cent today, two cents tomorrow, four cents the next day, eight cents the next, and so on, stopping with the last payment on June 21.

(a) Assuming you take this deal, how much money will you receive on June 21?

(b) Should you take the deal? Explain.

(c) Would you take the deal if payments continued for the entire month of June?