Black box model and Herbert-Pirt substrate distribution (10 points). In a strain of E. coli (X) grown on substrate S, the specific rate of substrate uptake can be described via the following Herbert-Pirt relationship: qs=0.20.03CmolXhmmolS Also, qs can be expressed in terms of Cs : qs=23+Cs0.15CsCmolXhmmolSwhereCshasunitsofmmol/L a. (2) At 0Cs10mmol/L, qs can be approximated as: a linear function of Cs a natural log function of Cs independent of Cs none of the above b. (2) At Cs>1000mmol/L,qs can be approximated as: q a linear function of Cs a natural log function of Cs independent of Cs none of the above c. (2) What is Cs at qs=21qsmax ? d. (3) What is Cs when =0 ? What fraction of S is used for maintenance when =0