Suppose that a room containing 1300 cubic feet of air is originally free of carbon monoxide (CO). Beginning at time t = 0, cigarette smoke containing 6% CO is introduced into the room at a rate of 0.8 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 state the initial condition. dA dt A(0) (B) Solve the IVP to find the amount of CO in the room at any time t > 0. A(t) = (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. t = minutes
Suppose that a room containing 1300 cubic feet of air is originally free of carbon monoxide (CO). Beginning at time t = 0, cigarette smoke containing 6% CO is introduced into the room at a rate of 0.8 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 state the initial condition. dA dt A(0) (B) Solve the IVP to find the amount of CO in the room at any time t > 0. A(t) = (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. t = minutes
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Suppose that a room containing 1300 cubic feet of air is originally free of carbon monoxide (CO). Beginning at
time t = 0, cigarette smoke containing 6% CO is introduced into the room at a rate of 0.8 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 state the initial condition.
dA
dt
A(0)
(B) Solve the IVP to find the amount of CO in the room at any time t > 0.
A(t) =
(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.
t
minutes
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