Problem 9 (Chemostat vs. batch reactor, 15 pts). Consider two different methods of producing biomass in bioreactors. In one method, you prepare a batch reactor by loading it with the necessary growth media and inoculating it with a mass m0 of bacterial biomass. The bacteria exhibit exponential growth with growth rate k. Once the bacteria have grown to biomass m, you empty the batch reactor and repeat the growth processes. The amount of time it takes to empty the batch reactor, reload it with growth media, and re-inoculate it with new bacteria (the turnaround time) is tturn. The biomass m is small enough that the bacteria are still exhibiting exponential growth, but large enough that mm0. In a second method, you instead use a chemostat (a CSTR) where the feed contains no biomass. Assume that for both the batch reactor and the chemostat there is plenty of substrate such that the growth rate k is constant and the same for both reactors. Show that the ratio of the production rate of biomass in the chemostat to that by batch processing is approximately ln(m/m0)+ktturn. Based on your analysis, which is more efficient