14. (-/4 Points) DETAILS BERRAPCALCBR7 6.5.059. MY NOTES ASK YOUR TEACHER Suppose that you now have $5000, you expect to save an additional $4000 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) years from now. (a) Write a differential equation that expresses the fact that your balance will grow by 4 (thousand dollars) and also by 10% of itself. (Hint: See the Predicting Wealth Example.] (b) Write an initial condition to say that at time zero the balance is 5 (thousand dollars). Y(O) = (c) Solve your differential equation and initial condition. (d) Use your solution to find your bank balance t = 20 years from now. (Round your answer to two decimal places.) thousand