I am having a hard time with this problem.

Let us first define our functions. Let p (t): rate of inflation, u (t): unemployment rate, q (t): expected rate of inflation. We will now consider the following three equations that model the interactions between inflation and unemployment during a certain time - period. p = a - bu + hq(0 , m = 3, determine the path of q(t) with q (0) = 3 and q' (0) = V29 20 Hint: Obtain a second order linear differential equation for q by eliminating p and u from the given three equations. 2. Using the path of q(t), determine the paths of p(t) and u(t) and then graph them on the same time axis. You may use a graphing software such as Desmos @ or Wolfram Alpha or something of your choice. 3. Based upon the graphs obtained in part (2), what can you tell about the relationship between the rates of inflation and unemployment? Write a summary in 3 - 4 sentences