For the simple metabolic production and degradation system: k A a) Please perform a material balance to determine the analytical solution for a(t) with the initial condition, a(t = 0) = A0. b) Next, please run a Euler's method simulation with a step size of 0.1 s over 5 s for the differential form of the material balance. Assume A0 = 1, r = 4, and k = 1. Finally, please show a plot comparing the analytical solution trace to the numerical simulation.