(Solution) - Each second 3 of the chemical in container 1 enters -(2025 Original AI-Free Solution)

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Each second, 3% of the chemical in container 1 enters container 2, and 10% of the chemical in container 2 returns to container 1 (compare with Exercise 4).
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.