Exercise 12 (Chapter Review)

Your magic chocolate bunnies reproduce like rabbits: every large bunny produces 2 new mini bunnies each day, and each day every mini bunny born the previous day grows into a large bunny. Assume you start with 2 mini bunnies and no bunny ever dies (or gets eaten).

1. Write out the first few terms of the sequence.

2. Give a recursive definition of the sequence and explain why it is correct.

3. Find a closed formula for the $n$th term of the sequence.