Prediction using Monod equation

Mathematical optimization always requires a deterministic process model to predict the future behavior of a process. However, as previously mentioned, it is difficult to construct mathematical models that can cover the entire range of fermentation due to the complexity of intracellular metabolic reactions. As an alternative to the deterministic mathematical models, Kishimoto et al. proposed a statistical procedirre that uses linear multiple regression models [7], as shown below, instead of a deterministic mathematical model such as a Monod equation. 

For a trial in whieh Fe(III) = 20 mM at time zero, prepare two plots, the first of whieh ean be used to assess the ability of the Monod model to aceurately reflect the experimental data tabulated below, and the second of which can be used to ascertain whether or not the system of interest exhibits auto-catalytic behavior. Plot Fe(II) versus time in hours for times from zero to 80 h starting with an initial cell level (Xq) of 1.5 X 1 o cells/L. Plot both the data and the curve predicted using the solution to the differential equations that correspond to the indicated parameter values. In addition, plot the reaction rate evaluated using equation (1) as a function of the time elapsed during the experiment. What conclusions can you draw fiom these plots ... 

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