3.  Every year Stephanie’s hamster population doubles. She started with 6 hamsters. How many hamsters does she have after 7 years? After n years?

4.  A person invests $1000 at 12 % interest compounded annually. Find the amount at the end of n years using a recurrence relation and initial conditions.

5. Solve the recurrence relation.

6.  An elf has a staircase of n stairs to climb. Each step it takes can cover either 1 stair or 2 stairs.  Find a recurrence relation for the number of different ways for the elf to ascent the n- staircase.

9.  Suppose we draw n straight lines on a piece of paper so that every pair of lines intersect, but no three lines intersect at a point.  The recurrence relation for the number of regions into which these n lines divide the plane is

11.  There are 3 pegs mounted on a board and n disks of various sizes with holes in their centers. Initially the disks are stacked from the largest to the smallest on one peg.  The goal is to move the entire tower to another peg. The rule is 1. You can move only one disk at a time. 2. You can not place a larger disk on a smaller one.  The recurrence relation is