The air in a crowded room full of people contains .25% carbon dioxide (CO₂). An air conditioner is turned on that blows fresh air into the room at the rate of 500 cubic feet per minute. The fresh air mixes with the stale air, and the mixture leaves the room at the rate of 500 cubic feet per minute. The fresh air contains .01% CO₂, and the room has a volume of 2500 cubic feet.

(a) Find a differential equation satisfied by the amount f (t) of CO₂ in the room at time t.

(b) The model developed in part (a) ignores the CO₂ produced by the respiration of the people in the room. Suppose that the people generate .08 cubic foot of CO₂ per minute. Modify the differential equation in part (a) to take into account this additional source of CO₂.