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Problem 46 Easy Difficulty

The air in a room with volume 180 $ m^3 $ contains $ 0.15% $ carbon dioxide initially. Fresher air with only $ 0.05% $ carbon dioxide flows into the room at a rate of 2 $ m^3/min $ and the mixed air flows out at the same rate. Find the percentage of carbon dioxide in the room as a function of time. What happens in the long run?

Answer

$p(t)=\frac{1}{20}\left(1+2 e^{-t / 90}\right)$

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Video Transcript

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