In year one, an investor deposits 3 dollars in her bank account. Each year after that, the balance in the account triples, but a bank fee is paid at the end of the year. The bank fee is 2 dollars at the end of year two, and the bank fee doubles every year after that. Let A(n) be the account balance at the end of year n 1. Give a recursive definition for A(n), including any necessary base cases. Solve the recurrence and prove your result using induction.