Problem 1: Consider a microbial bioreactor operating in batch mode. Assume that volume is constant. a) Write a material balance for biomass and obtain an ODE representing the dynamics of the biomass concentration inside the reactor. Assume that growth rate follows Monod kinetics. b) Write a material balance for substrate and obtain an ODE representing the dynamics of the biomass concentration inside the reactor. Assume that substrate consumption rate follows first-order kinetics ( rs=kS)