Consider a biochemical reaction in which a certain substance is both produced and consumed. The concentration of this substance at time t is defined...

Consider a biochemical reaction in which a certain substance is both produced and consumed. The concentration of this substance at time t is defined to be c(t). Assume that the function c obeys the following differential equation: dc/dt = Kmax (c / k + c) − rc Where Kmax, k, and r are all positive constants. The first term on the right hand side of this equation denotes the concentration-dependent production and the second denotes the consumption. (a) What is the maximal rate at which the substance is produced? (b) At what concentration is the production rate 50% of this maximum value? (c) If the production is turned off, the substance decays. How long will it take for the concentration to drop by 50%? (d) At what concentration does production balance consumption?