Q$2.$ Deriving and Implementing Model Equations for Fed$-$batch Mode FermentationAssume that you have one type of microorganism growing on a single substrate and producing a single product P in a stirred tank bioreactor using a fed$-$batch mode of operation. X and S show cell$/$biomass and substrate concentrations, respectively. The reactor is fed with fresh substrate at concentration Sin and volumetric inflow rate Qin.a$)$ Give the model equations $($Modify the equations we derived in the lecture based on your chosen growth model in Q$1).$b$)$ Implement and simulate the model equations using a MATLAB script $($Modifythe code provided in the lecture$).$ Use the parameters obtained in Q$1.$ Please provide the code you used$\mathrm{.}1$