Exercise 9.

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.

1. Find both a recursive and closed formula for how many Skittles the nth customer gets.

2. Check your solution for the closed formula by solving the recurrence relation using the Characteristic Root technique.