A 25 Liter batch reactor is filled with sterile growth medium and inoculated with 2.5 grams of E. Coli. Adequate oxygen is supplied and there is enough glucose and other nutrients such that growth is not limited during the initial growth phase. Under these conditions, the first order reaction rate constant is measured as k=0.075 hr-1.

a) Derive an expression for concentration as a function of time.

b) Plot the concentration vs. time for the first 48 hours of growth. Be sure to properly label the axes.

c) Find the total mass of cells in the reactor after 48 hours.