1. Continuous random walk (the diffusion equation): In class, we derived that the density of swimming bacteria, (z,t), satisfies the diffusion equation: a) Show that ADt is a solution of the diffusion equation for any constant zo. What does zo represent? (b) Using Matlab or other graphing software, plot plx, t for D 1 and o 0, fort1 3, 10, 40, Use-20 z 20 for the bounds on. and plot all four curves on the same graph. What happens as t increases