The discrete-time dynamical system of a lung with absorption is given by the following equation. ct + 1 = (1 - 1* q) * (1 - 1*α)*ct + γ* q. In this equation q denotes the fraction of air that is expelled with each breath, c denotes the concentration of the chemical you are considering in the lungs, α is the fraction of the chemical that is absorbed with each breath, and γ denotes the ambient concentration of the chemical in the atmosphere. An animal is living in a cave and the air in the cave contains a certain chemical we are interested in studying. Suppose the animal has a lung capacity of 10 liters and exhales .9 liters of air with each breath. The animal absorbs 10% of the chemical in its lungs with each breath, and at equilibrium, the concentration of the chemical in the animal's lungs is 2.3%. Determine the ambient concentration γ of the chemical in the air in the cave.