$3.)$ You are running an enzyme assay. You add $1{10}^{-2}M$ substrate $S$ to a preparation of $1{10}^{-7}M$ enzyme $E_0.$ The reaction follows the mechanism below:

$E+$SharrES $E+P$

Where $k_1$ is the rate constant for the forward reaction to form ES$,k_{-1}$ is the rate constant of the dissociation of ES$,$ and $k_2$ is the rate constant of product formation.

The values of the rate constants are:

$k_1={10}^6{M}^{-1}se{c}^{-1}$

$k_{-1}=1000se{c}^{-1}$

$k_2=10se{c}^{-1}$

$($a$)$ At steady state, there is no change in the concentration of enzyme substrate complex concentration over time $($i$.$e$.,d\frac{ES}{d}t=0.$ Using the values provided, determine the concentration of ES at steady state for this reaction.

$($b$)$ What is the overall reaction velocity $($i$.$e$.,v=d\frac{P}{d}t)$ for this reaction?

$($c$)$ Based on the information given, calculate $K_m$ and $V_{\text{m}\text{a}\text{x}}$ for this reaction.