Please solve it mathematically.

Problem 4 - Ventilation system failure. In Lecture 9 , and in recitation 3 , we explored different ventilation scenarios using the model we developed in class. This problem asks you to consider one of the scenarios we discussed but didn't analyze - the failure of the ventilation system's ability to bring fresh air into the room. Assume the system worked correctly with no students present and broke the moment the students showed up. The classroom has a volume of 2.8106L, with 100 students producing CO2 at a rate of 0.1lb CO2/hr. The ambient air outside has a CO2 concentration of 400ppm=1.7106lbCO2/L, and room initially has the same concentration of CO2. Before the ventilation system failed, it provided 3ACPH. The room remains a constant pressure. Assume the room's conditions are 1atm and 20C. Do not consider oxygen in this model. a) Develop a model (starting from the conservation equation) for the concentration of CO2 in the classroom. b) Determine the steady state concentration of CO2 and determine the amount of time students can be