Batch fermentation
For aerobic cultivation of yeast the cell mass concentration, X_{t}, and the concentration of the limiting substrate component (glucose), S_{t}, has been determined.
Time (min)

0

30

60

90

120

150

180

210

240

X_{t} (gDCM*/l)

5.0

5.2

6.6

8.4

10.8

13.8

17.7

19.0

20.0

S_{t }( g glu/l)

30.0

29.6

26.8

23.2

18.4

12.4

4.6

2.0

0.0

*Dry Cell Mass
a. Calculate the average cell mass yield factor, Y_{X/S }in this fermentation.
b. Calculate the maximum specific growth rate, mMAX, in the logarithmic growth phase.
c. Calculate the volumetric growth rate, dX/dt = r_{X} at time=125 min.
d. Calculate the volumetric substrate utilization rate, r_{S}, and the specific substrate utilization rate, q_{S}, of the yeast at time = 170 min, assuming that the average yield factor can be used to determine r_{S}.
e.Calculate the concentration of left over substrate at time = 130, again assuming that the average yield factor can be used.