Think back to the magical candy machine at your neighborhood grocery store. Suppose that the first time a quarter is put into the machine 1 Skittle comes out. The second time, 4 Skittles, the third time 16 Skittles, the fourth time 64 Skittles, etc. a) Find both a recursive and closed formula for how many Skittles the nth customer gets. b) Check your solution for the closed formula by solving the recurrence relation using the Characteristic Root technique.

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