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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?

Name: the air in a room with volume 180 m3 contains 015 carbon dioxide initially fresher air with only 005
Uploaded: 2020-05-23
Duration: 3 min 33 s
Channel: Numerade
Description: 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

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

Topics

Differential Equations

Calculus: Early Transcendentals

Chapter 9

Differential Equations

Section 3

Separable Equations

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Video Transcript

the problem. Every aunt let me take you. Wait! You want to fight? See you flow in a and Tomi. Thank you. Wait! Its descent. They sentence. That is parentally Endeavour. You know what? Really? Why? But one d? Because it's is a people say not to amount, forgets or really equal, do you? In the Taliban, is it fine over when? Indeed it is minus two x over. Therefore we have for them as decks upon 20 people 200.5 minus 6/90 or nutritional digs. Find minus six people in a position. Dede 4 90 cities, 11 more. Want five minus six over minus one. Equal one on 98. Now this equal do more than 15 minus six equal. Minus city for 90 minus. No, we have this equal. They wanted you to find minus six. It will give the power Manistee upon 90 into the bar. Lunacy that is equal to indeed ar minus department Anti our limits equal Did a 0.5 minus indeed you the power minus t about 90. Therefore, this is only Steve and we have it's due to equal. Didn't want to do this. Five minus the So this implies the well minus 0.10 Therefore further we have it's t equal. Dearborn. Deal five. Let us get one. You the power minus T upon 90. This is done, sir, to give in.

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