4. A mysterious document had been discovered in F¨uhrerbunker inBerlin and Robert Langdon was urgently called to investigate. Aspart of his top secret mission, at midnight he goes into aconcealed archival chamber, which is sealed off from the rest ofthe facility by a hermetical door that will be reopened at exactly6 am. The chamber has the volume of 2000 m3 and a primitive aircirculation system with air pumped in and out at the rate of 1000L/min. Prof. Langdon only needs two hours to examine the document.Unbeknownst to him, an agent of the powerful Rote Hakenkreuz secretsociety had infiltrated the security, and has managed to connect asource of carbon monoxide (CO) to the air intake. The poisonous gasis dispersed uniformly and the mixture is continuously removed viathe air outflow. (a) Assuming that the concenration of CO in theair inflow is 0.5%, or 5000 ppm (parts per million), write down adifferential equation for the amount A(t) of CO in the chamber as afunction of time. (b) At midnight, the concentration of CO in thechamber is already 200 ppm. Set up and solve the initial valueproblem for A(t). (c) As a former diver, Langdon can tolerate up to480 ppm of CO while maintaining his mental acuity and up to 1000ppm before he passes out. Will the professor survive this ordealand complete his mission?
