Non$-$linear regression using gradient descent $($solver$)$

$35$

The following data points have been provided to you from a set of experiment investigating the kinetics of the enzyme invertase. Invertase catalyzes the hydrolysis of sucrose to glucose and fructose. Interestingly, at high substrate concentrations, the rate of reaction goes up with substrate concentration and then begins to decrease, as the substrate begins to inhibit the reaction that converts it$.$

Below are two equations that describe different types of enzymatic inhibition. In the case of Invertase and Sucrose, we will assume that $C_i=C_a,$ and $K_i=K_m.$

Competitive Inhibition

$r_p=\frac{V_{\text{m}\text{a}\text{x}}{C}_A}{C_A+K_m(1+\frac{C_1}{K_1})}$

$\backslash$table$[[\backslash$table$[[$Substrate$],[$Concentration Ca$],[(gmol{m}^{-3})$