Cigarette smoke contains carbon monoxide as well as other noxious compounds. Consider a small room of volume V m3. Let f be the rate of air exchange in cubic meters pci mmuk Let mil) be the mass in milligrams of carbon monoxide in the room. Write an initial-value problem for the mass of carbon monoxide in the room. Assume that the initial amount is mo mg. No more carbon monoxide is introduced in the room after time zero. Carbon monoxide leaves the room via the air exchange between the room and its environment; the concentration of carbon monoxide in the room in milligrams per cubic meter can be determined from the mass of carbon monoxide and the room volume. Solve the initial-value problem from part a. C oncentrations of trace chemicals are often measured in parts per million (ppm). For example, 50 ppm means that every I million molecules includes 50 of carbon monoxide, which translates to a volume equal to 50 millionths of the room volume. The OSHA standard for maximum allowable carbon monoxide concentration in a room where people will spend X h/day is 50 ppm. Let Pit) be the concentration of carbon monoxide in pails per million Use the answer from part h to determine Pit) for the case where m0 corresponds to a concentration of 50 ppm. Use the fact that I $$ of carbon monoxide gas occupies a volume of 0.86 in at standard room temperature and atmospheric pressure. d. ( onsidei a small office- of volume 25 m\ Prior to 1999. the EPA regulations for a large office building required a flow rate of 0.14 in Vmin per person. (In 1999. the requirement was increased by a factor of 4.) Our hypothetical small office is an appropriate size for one person. Assuming this flow rate, how long does it take for the concentration m'dron from 50 ppm down to a relatively safe level of 5 ppm?