This question has several parts that must be completed sequentially. If you skip a part of the question, you will not receive any points for the skipped part, and you will not be able to come back to the skipped part. Tutorial Exercise An annuity is a fund into which one makes equal payments at regular intervals. If the fund earns interest at rate r compounded continuously, and deposits are made continuously at the rate of d dollars per year (a continuous annuity), then the value y(t) of the fund after t years satisfies the differential equation y' = d + ry. + (Do you see why?) Solve the differential equation for the continuous annuity y(t) with deposit rate d = $8000 and continuous interest rate r = 0.04, subject to the initial condition y(0) = 0 (zero initial value). Step 1 The first step is to rewrite the equation with the differential as _= 8000 + 0.04y. Now, separate the dt variables with all functions of y (including the differential dy) alone on one side of the equation and the constant and all functions of t (including dt) on the other side. Factoring the right hand side and separating the variables, we have dy = 0.04 dt x dy = 0.04 dt. X