In the problem we will look at a situation in which models similar to the predatorprey population models arise Suppose A and B represent two substances that can combine to form a new substance C chemists would write A B C Suppose we have a container with a solution containing low concentrations of substances A and B and A and B molecules react only when they happen to come close to each other If and represent the amount of A and B in the solution respectively then the chance that a molecule of A is close to a molecule of B at time is proportional to the product Hence the rate of reaction A and B to form C is proportional to Suppose C precipitates out of the solution as soon as it is formed and the solution is always kept well mixed A system of differential equations that models the evolution of and is given by You should form your equations above so that the reaction rate parameter is and that the value of is assumed to be positive Now suppose that the substances A and B are added to the solution at the constant rates of units of A per unit time and units of B per unit time A modification to the system above that incorporates this assumption is Now suppose that in addition to the A B C reaction a reaction A A D also can occur when two molecules of A are close and substance D precipitates out of the solution A modification to our most recent system above that also incorporates this assumption use as the reaction rate parameter for this new reaction is Now suppose that in addition to the A B C and A A D actions we also have the potential for the reaction B B A which has reaction rate parameter A modification to our most recent system above that also incorporates this assumption is Be careful this last reaction isnt just a new way to lose substance B but also to gain substance A