Question: (Continuation of Problem.) Government agencies warn that exposure to air containing 0.02% carbon monoxide can lead to headaches and dizziness. How long does it take for the concentration of carbon monoxide in the room in Problem to reach this level?
Problem: When people smoke, carbon monoxide is released into the air. In a room of volume 60 m3, air containing 5% carbon monoxide is introduced at a rate of 0.002 m3/min. (This means that 5% of the volume of the incoming air is carbon monoxide.) The carbon monoxide mixes immediately with the rest of the air, and the mixture leaves the room at the same rate as it enters.
(a) Write a differential equation for c(t), the concentration of carbon monoxide at time t, in minutes.
(b) Solve the differential equation, assuming there is no carbon monoxide in the room initially.
(c) What happens to the value of c(t) in the long run?