Suppose that you now have $9000, you expect to save an additional $3000 during each year, and all of this is deposited in a bank paying 10% interest compounded continuously. Let y(t) be your bank balance (in thousands of dollars) tyears from now. (a) Write a differential equation that expresses the fact that your balance will grow by 3 (thousand dollars) and also by 10% of itself. [Hint See the Predicting Wealth Example] y: X (b) Write an initial condition to say that at time zero the balance is 9 (thousand dollars). y(0) = (c) Solve your differential equation and initial condition. y (d) Use your solution to nd your bank balance t = 25 years from now, (Round your answer to two decimal places.) $ thousand