A lung follows the discrete-time dynamical system ct+1 = f(ct). We know only that neither ct+1 nor

Question:

A lung follows the discrete-time dynamical system ct+1 = f(ct). We know only that neither ct+1 nor ct can exceed 1 mole/liter. Use the Intermediate Value Theorem to show that this discrete-time dynamical system must have an equilibrium.
The Intermediate Value Theorem can often be used to prove that complicated discrete-time dynamical systems have equilibria.