A classmate, Sam, is opening a savings account that has an annual interest rate of 5%. She has $10,000 to open the account with and she will be making no other deposits. Every month, she will be withdrawing $200. (Hint: pay attention to time units here!)

(a) Build an IVP that models the change in the amount of money in Sam's account per year.

(b) Find the amount of money in the account at any time t.

(c) How long until the account is empty? (Express your answer correct to one decimal place.)