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Answer:
Explanation:
The concentration of CO2 in the room will be the amount of CO2 in the room at time t, divided by the volume of the room.
Let A(t) be the amount of CO2 in the room, in ft3 CO2.
The air entering the room is 3000 ft3/min with 0.06% concentrarion of CO2. That can be expressed as (3000*0.06/100)=1.8 ft3 CO2/min.
The mixture leaves at 3000 ft3/min but with concentration A(t)/V. We can express the amount of CO2 leaving the room at any time is A(t).
We can write this as a differential equation
We can rearrange and integrate
We also know that A(0) = 12000*(0.3/100)=36 ft3 CO2.
Then we have the amount A(t) as