Each second, 30% of the chemical in container 1 enters container 2, and 20% of the chemical in container 2 returns to container 1 (compare with Exercise 3).
In many ways, probabilities act like fluids. For each of the following models of chemical exchange, let ct represent the amount in container 1 and dt the amount in container 2 at time t. Write a discrete-time dynamical system for the amount of chemical in each container. Define pt to be the fraction of chemical in container 1, and write a discrete-time dynamical system giving pt+1 as a function of pt. Find the equilibrium fraction of chemical in the first container.