Let y(t) represent your retirement account balance, in dollars, after it years. Each year the account earns 4% interest, and you deposit 4% of your annual income. Your current annual income is $42000, but it is growing at a continuous rate of 2% per year. Write the differential equation modeling this situation. dy_ E Let y(t) represent your bank account balance, in dollars, after 1' years. Suppose you start with $90,000 in the account. Each year the account earns 5% interest, and you withdraw 59000. Write the differential equation modeling this situation. El l dt Solve the differential equation exactly to find the exact amount of money in the account after 5 years. ' ' dollars Suppose you deposit $7500 into an savings account earning 5% annual interest compounded continuously. To pay for all your music downloads, each year you withdraw $800 in a continuous way. Let A(t) represent the amount of money in your savings account it years after your initial deposit. (A) Write the DE model for the time rate of change of money in the account. Also state the initial condition. dA a=i i me: (E) Solve the IVP to find the amount of money in the account as a function of time. A(t) = i i (C) When will your money run out? t = ' 'years