3. The growth of bacteria (N cells) in a chemostat can be modeled as: dN =kN dt where k = 3 h is a first order rate constant a show that N(t) = Noekt is the solution to this differential equation, where No = N(t = 0). b. For k = 3 h 1, find the time required for the number of bacteria to double. C. A more realistic growth model, called the logistic model, is dN dt = kw (1-4) =kN The factor in the parenthesis reflects that fact that bacteria slow their growth when they get too crowded. Find the two steady-state solutions for the logistic model. d. Show by substitution or integration that the solution for Nt) in the logistic model is N(t) =. (ekt - 1) + 1 e. Sketch (or use Excel) a plot of (t)/N, vs. t for each model on a single plot. Assume a = 10N, = for the logistic model. Show where 1 and 10 are on the N(t)/No-axis and where 1/k is on the t- axis. Noekt