Open Question: Applications of first order linear ODEs. Calculus?
Question is:
An office contains 1000 ft^3 of air initially free of carbon monoxide. Starting at time = 0, cigarette smoke containing 4% carbon monoxide is blown into the room at the rate of 0.5 ft^3/min. A ceiling fan keeps the air in the room well circulated and the air leaves the room at the same rate of 0.5ft^3/min. Find the time when the concentration of carbon monoxide reaches 0.01%.
An office contains 1000 ft^3 of air initially free of carbon monoxide. Starting at time = 0, cigarette smoke containing 4% carbon monoxide is blown into the room at the rate of 0.5 ft^3/min. A ceiling fan keeps the air in the room well circulated and the air leaves the room at the same rate of 0.5ft^3/min. Find the time when the concentration of carbon monoxide reaches 0.01%.
I'm always having trouble setting up this equation
I know s = smoke;
so DS/dt = in - out
[4% * 0.5ft^3/min] - [0.01% * 0.5ft^3/min ] I know I'm missing some variables such as t, to find the time when concentration of smoke is 0.01%
My assumption is 4% of 1000ft^3 so that there is 9060ft^3 = air while 40ft^3 = smoke in.
0.01% of 1000 is 9090 = air and 10 = smoke.
Just need help setting up the question and understanding how to get it.
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