Four thousand dollars is deposited into a savings account at 4.5% interest compounded continuously.

(a) What is the formula for A(t), the balance after t years?

(b) What differential equation is satisfied by A(t), the balance after t years?

(c) How much money will be in the account after 6 years?

(d) When will the balance reach $8000?

(e) How fast is the balance growing when it reaches $8000?