A bank account earns 7% annual interest compounded continuously. You deposit $10,000 in the account, and withdraw money continuously from the account at a rate of $1000 per year.
(a) Write a differential equation for the balance, B, in the account after t years.
(b) What is the equilibrium solution to the differential equation? (This is the amount that must be deposited now for the balance to stay the same over the years.)
(c) Find the solution to the differential equation.
(d) How much is in the account after 5 years?
(e) Graph the solution. What happens to the balance in the long run?