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 .6 liters of air with each breath. The ambient concentration of the chemical in the air in the cave is .031, in other words, 3.1% of the air in the cave consists of the chemical. At equilibrium, the concentration of the chemical in the animal's lungs is .018, in other words, 1.8% of the air in the animal's lungs consists of the chemical. What is the fraction of the chemical that is absorbed with each breath by the animal? Your answer for α should be written as a decimal, not as a percent.