LW Exercise 2.

The unsaturated first order process in the plot above has concentration functions (see RK Exercise 4):

(a) Let x = S(t) and y = P'(t). Compute P'(t) and then rewrite it as a (parabolic) function of x, i.e. y = f(x).
 
 
 
 
 
 
 
 
 
 

(b) Find the x-intercepts of the parabola in (a) and the coordinates of its vertex.
 
 
 
 
 
 
 
 
 

(c) On the plot below, sketch a graph of the parabola labeling it with the information found in (b).

The saturated Michaelis-Menten process in the plot at the top of the previous page has concentration functions (see LW Definition 2, Example 1):

(d) Let x = S(t) and y = P'(t). Compute P'(t) and then rewrite it as a (hyperbolic) function of x, i.e. y = f(x).
 
 
 
 
 
 
 
 

(e) Find the vertical and horizontal asymptotes of the hyperbola in (d) by taking appropriate limits.
 
 
 
 
 
 
 
 

(f) On the same plot above that you sketched the parabola, also sketch the hyperbola labeling it with the information found in (e).