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 5% CO is introduced into the room at a rate of 0.6 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. 0.6(0.05 d.A dt A(0) = = 0 A 1300 (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 5% CO is introduced into the room at a rate of 0.6 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. 0.6(0.05 d.A dt A(0) = = 0 A 1300 (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
Chapter6: Exponential And Logarithmic Functions
Section6.1: Exponential Functions
Problem 60SE: The formula for the amount A in an investmentaccount with a nominal interest rate r at any timet is...
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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 5% CO is introduced into the room at a rate
of 0.6 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.
0.6(0.05-1300)
dA
dt
A(0)
= 0
(B) Solve the IVP to find the amount of CO in the room at any time t > 0.
A(t) =
t
OF
(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
=
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