EK Exercise 2.1.

EK Exercise 2.2.
Next, show that the equations:

can be derived, by using the equation for C(t) derived in EK Exercise2.1 above, together with the equations:

EK Exercise 2.3.
Show that when the P'(t) is half maximal, i.e. P'(t) = 0.5 x Vm, for some value of t, then the substrate level S(t) turns out to be equal to Km, for that same value of t. So, first substitute P'(t) = 0.5 x Vm into the Michaelis-Menten equation for P'(t) and then solve for S:

EK Exercise 2.4.
Define S(t) and P(t) using Lambert's W function, as in LW Exercise 1.4:

and then show that S(t) and P(t) satisfy the Michaelis-Menten Uptake equations.
 
 
 
 
 
 
 
 
 
 
 
 
 
 

EK Exercise 2.5.
Also, define S(t) and P(t) using Lambert's W function, as in LW Exercise 1.6:

and then show that S(t) and P(t) satisfy the Michaelis-Menten Uptake equations. Which of the two different definitions of S(t) and P(t), given here in and in the last problem above, provide the best model? Explain why you would choose one over the other.