Suppose that a room containing 1900 cubic feet of air is originally free of carbon monoxide (CO). Beginning at time $\displaystyle {t}={0}$, cigarette smoke containing 6% CO is introduced into the room at a rate of 0.2 cubic feet per minute. The well-circulated smoke and air mixture is allowed to leave the room at the same rate.

Let $\displaystyle {A}{\left({t}\right)}$ represent the amount of CO in the room (in cubic feet) after $\displaystyle {t}$ minutes.


(A) Write the DE model for the time rate of change of CO in the room. Also state the initial condition.
$\displaystyle \frac{{{d}{A}}}{{{\left.{d}{t}\right.}}}=$ Preview Question 6 Part 1 of 4  
$\displaystyle {A}{\left({0}\right)}=$


(B) Solve the IVP to find the amount of CO in the room at any time $\displaystyle {t}>{0}$.
$\displaystyle {A}{\left({t}\right)}=$ Preview Question 6 Part 3 of 4  


(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.
$\displaystyle {t}=$ minutes Preview Question 6 Part 4 of 4