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 4% 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 4% 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
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 13EQ
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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 4% 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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