For the data given in Question $2$ of Homework I $($ethanol production by S$.$ cerevisiae over time$)$

a$)$ Use the linearized Michaelis$-$Menten model $($Lineweaver$-$Burk equation$)$ derived in the class and Gauss$-$Jordan elimination to predict model parameters $K_m$ and $V_{\text{m}\text{a}\text{x}\text{.}}.$ Calculate also $R^2$ using the formula given in the class. Compare the model performance with the linear and cubic models you constructed in Homework I, discuss.

b$)$ For the following nonlinear model $),$ derive the equations and terms required for Newton$-$Raphson based iterative solution of fitting the nonlinear Michaelis$-$Menten model to the given data, including the terms of the Jacobian matrix. Show all your steps. Do not attempt to solve the problem.

$\backslash$table$[[\backslash$table$[[$Time$],[($hour$)]],$Ethanol $($g$/$L$)],[2,1],[4,4],[6,10],[8,18],[10,25],[12,27]]$