Differential equations Suppose that a room containing 1100 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 0.1 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
Differential equations
Suppose that a room containing 1100 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 0.1 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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