Suppose that a room containing 1000 cubic feet of air is originally free of carbon monoxide. Beginning at time $\displaystyle {t}={0}$ cigarette smoke, containing 4 % carbon monoxide, is introduced into the room at a rate of 0.1 cubic ft/min, and the well-circulated mixture is allowed to leave the room at the same rate.

(a) Find an expression for the concentration $\displaystyle {y}$ of carbon monoxide in the room at any time $\displaystyle {t}$.

$\displaystyle {y}$ =

Hint: Since concentration = amount/volume it may be easier to first find the expression that describes the amount of carbon monoxide. If that expression is $\displaystyle {Q}$, then $\displaystyle {y}={Q}$/volume.

(b) Extended exposure to a carbon monoxide concentration as low as 0.00012 is harmful to the human body. Find the time $\displaystyle {t}$ at which this concentration is reached.

$\displaystyle {t}$ =