$\"\"$

\

The volume of the room is $\"\"$ .

\

The percentage of carbon dioxide initilly is $\"\"$ .

\

The percentage of carbon dioxide contain in the fresh air is $\"\"$

\

The rate of carbon dioxide flows is $\"\"$ .

\

The rate of mixed air flows is $\"\"$ .

\

Let $\"\"$ be the amount of carbon dioxide after $\"\"$ minutes.

\

Rate of change in carbon dioxide is the percentage of carbon dioxide coming into the room minus percentage of carbon dioxide going out of the room.

\

Rate of change in carbon dioxide is $\"\"$ .

\

Rate of carbon dioxide coming into the room is $\"\"$ .

\

Rate of carbon dioxide going out of the room is $\"\"$ .

\

$\"\"$

\

Substitute corresponding vakues in the above equation.

\

$\"\"$

\

Apply integration on each side.

\

$\"\"$

\

Let $\"\"$ then $\"\"$ .

\

$\"\"$

\

Substitute $\"\"$ inthe above equation.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

Substitute $\"\"$ and $\"\"$ in the above equation.

\

$\"\"$

\

Substitute $\"\"$ in $\"\"$ .

\

$\"\"$

\

$\"\"$

\

The percentage of carbon dioxide in the room as a function of time is $\"\"$ . $\"\"$

\

Find what happen in long run.

\

$\"\"$

\

$\"\"$

\

$\"\"$

\

The percentage of carbon dioxide in long run is $\"\"$ .

\

$\"\"$

\

The percentage of carbon dioxide in the room as a function of time is $\"\"$ .

\

The percentage of carbon dioxide in long run is $\"\"$ .