I have no idea what 0.0a is. I was thinking it might be typo. I'm not even sure where I'm suppose to start with this problem.
The residual and tidal volumes are important to consider. Assume that an allergen is in an aerosol form (1.0g/L air) and can be inspired and expired at the same rate a normal air. When first exposed to the allergen, how long will it take to reach equilibrium cocentration in the lung? Develop a graph of the concentration as a function of time.
Then assume the allergen binds and unbinds to the lung tissue at a first order rate of 0.0a /day. Predict the mass of bound allergen as a function for a 10 day exposure to allergen free air.