1. Consider the Hayes equation x(t) = ax(t) + bx(t t). 1.a Calculate the right most characteristic root (eigenvalue) when a = 1, b = 1, t= 1. (10 points) 1.b Calculate the right most characteristic roots (eigenvalues) when a = 0, b = /2, t= 1. (10 points) 1.c Consider the initial condition x(t) = t for t = [-7, 0] and the delay = 1. Solve the Hayes equation numerically over the interval t = [0, 50] for the following parameter combinations a=-1.1, b = 1, a=-0.9, b= 1, a=-0.1, b=-/2, a = 0.1, b = -/2, and comment your results. (10 points)