A lung follows the discrete-time dynamical system ct+1 = 0.75(ct)ct + 0.25 where = 5.0 and

A lung follows the discrete-time dynamical system ct+1 = 0.75α(ct)ct + 0.25γ where γ = 5.0 and the function α(ct) is positive, decreasing, and α(0) = 1. Show that there is an equilibrium between 0 and γ.
The Intermediate Value Theorem can often be used to prove that complicated discrete-time dynamical systems have equilibria.