2. Chemical Experiment: Consider an experiment in a chemistry lab, where two molecules of chemical A combine to form one molecule of chemical X. Chemical X is unstable and decays into two copies of A, at a rate proportional to its abundance, with coefficient p. During the experiment, chemical A is added into the mixture at a constant rate a. Also, chemical X is removed from the experiment at a rate proportional to its abundance, with coefficient y. You may assume that molecules of A combine according to a mass action law, with mass action coefficient k. KA 2 2A Z X Assume that a, M, Y, k > 0. a. Give differential equations that describe the system. b. Find any equilibria. c. Rescale the system to reduce the number of parameters. (Do it so that the rescaled equation for A has no parameters (i.e. the coefficients are all 1 or -1), and the rescaled equation for X has two parameters that are expressed in terms of a, A, Y, k.)