Hello. I need a help again for my differential equations class.(adsbygoogle = window.adsbygoogle || []).push({});

The problem is as follows:

The air in a room whose volume is 10,000 cu ft tests 0.15% carbon dioxide. Starting at t=0, outside air testing 0.05% carbon dioxide is admitted at the rate of 5000 cu ft/min.

(a) What is the percentage of carbon dioxide in the air in the room after 3 min?

(b) When does the air in the room test 0.1% carbon dioxide.

This problem is given after I studied the mathematical formulation of

[tex]\frac{dx}{dt}=IN - OUT[/tex]

I tried to write an equation using the above formula, but since there is no air coming out, I did not know how to write the euqation. The equation I wrote was

[tex]\frac{dx}{dt} = 2.5 ( ? unit/cu ft)(5000 cu ft/min) - 0[/tex]

I obtained 2.5 from multiplying 5000 by 0.0005. I don't even know if this is right. What I was trying to find was the amount of carbon dioxide in 1 cu ft.

Since no air is coming out, 0 is applied in the OUT section.

This does not seem to be right since the density of the air should be increased but there is no place that represent the change in my equation.

Will someone help me?

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# The percentage of carbon dioxide in the air

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