Problem 2: (Modeling) In a chemical reaction, one mole of substance A reacts with one mole of substance B to create one mole of product P. According to the law of mass action, the rate of production of P is proportional to the product of the concentrations of substances A and B. According to this principle, the time evolution of the concentrations of A, B and P, denoted by (105), b(t), and 1905), can be described by the differential equations dp da db a Imb, a k:ab et a kab, where k > 0 is the rate constant. The concentrations cannot be negative. Denote the initial conditions as a(0) : a0, b(0) : b0 and p(0) : p0. i. Show that the system of three equations can be reduced to the single equation where 5. and EN) are constants. Express the constants EL and E in terms of the initial concentrations 04], be and p0. ii. From now on, assume that do OO p(t) as predicted by the phase-line diagram in (ii)? iv. Solve the ODE in (i) with initial condition 19(0) 2 0 and always assuming that (L0