Question

Suppose that a room containing 1900 cubic feet of air is originally free of carbon monoxide (CO). Beginning at time t 0, cigarette smoke containing 3% CO is introduced into the room at a rate of 0.3 cubic feet per minute. The well- circulated smoke and air mixture is allowed to leave the room at the same rate. Let A(t) represent the amount of CO in the room (in cubic feet) after t minutes. (A) Write the DE model for the time rate of change of CO in the room. Also dA state the initial condition. Preview dt A(0) (B) Solve the IVP to find the amount of CO in the room at any time t > 0. A(t) Preview (C) Extended exposure to a CO concentration as low as 0.00012 is harmful to the human body. Find the time at which this concentration is reached. minutes Preview t

Answer 1

let AlH prnt the amountof co in o0m 0.3 A (0.03) L0.3) Thn dAlH 1900 0.3A wh.Alo) 1900 0, 0.009 dA dt 0.2 dt 3t 1900 e dA 0.3A t z 0.009 1900 quuval toluhon 0 009 () dt +C ALTF) 0.1 Ae 1900 O.36 1900 9.3 Ae 00 O O09 24 THU 0.3 0.3t oobt 9.31 A e 00 57 e 140o+C Ato) 0 C+S720 C-SA 0-3tu A e 1900 e = v= Al oar s 0 3t100 1-e )

(1-e T900 The loncentraton is H 1900 1900 O3t T900 2t 0.03(1-e whuxtt0.00012 gien) 0.3t1900) 1-e 1.0.0 031 1900) (1-e 0.00012 d.004 -0.It1900 e 0-996 1-0.004 J Ineo.3t1900 Inlo.996) In (0.996) 03t 1900 -1900 In (0 496). 25.38 4 in 22 TUE