A rather simple-minded approach to modeling synchronous culture is to assume that substrate uptake will be proportional to the number of organisms. Our equation for rate of change of substrate is:
dS/dt = -K × X
where S = concentration of limiting nutrient
K = some coefficient
X = concentration of organisms
The number of organisms doubles at regular time intervals. This is shown in the figure below drawn by the program SYNCH.BAS. Inspection of the program reveals some tricks to prevent S from going negative because the cells have a doubling time not dependent on substrate concentration.
Think about the graph and try the following:
Dept. of Chemical Engr.