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WAMAPhttps ![wwamap org/assess2rad-22966&aid-1114574#,HW #2 (1.1/71.2) Score: 3/14 0/11 answeredQuestion 11Suppose that a roomn containing 1100 cubic feet of ai...

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WAMAPhttps ![wwamap org/assess2rad-22966&aid-1114574#,HW #2 (1.1/71.2) Score: 3/14 0/11 answeredQuestion 11Suppose that a roomn containing 1100 cubic feet of air is originally free of carbon monoxide (CO): Beginning at time 0, cigarette smoke containing 6% CO introduced into the room ata 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 A(t) represent the amount of CO in the room (in cubic feet) after = Minutes:(A)

WAMAP https ![wwamap org/assess2rad-22966&aid-1114574#, HW #2 (1.1/71.2) Score: 3/14 0/11 answered Question 11 Suppose that a roomn containing 1100 cubic feet of air is originally free of carbon monoxide (CO): Beginning at time 0, cigarette smoke containing 6% CO introduced into the room ata 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 A(t) represent the amount of CO in the room (in cubic feet) after = Minutes: (A) Write the DE model for the time rate of change CO in the room Also state the initial condition: A(O) (B) Solve the IVP to find the amount 0f CO in the room at any time A(t) Extended exposure tQ CO concentration low ds 0.0C0IZ harmfull to the human body: Find the time at which this concentration reached: minutes Submit Questicl



Answers

The air in a crowded room full of people contains $.25 \%$ carbon dioxide $\left(\mathrm{CO}_{2}\right) .$ An air conditioner is turned on that blows fresh air into the room at the rate of 500 cubic feet per minute. The fresh air mixes with the stale air, and the mixture leaves the room at the rate of 500 cubic feet per minute. The fresh air contains $.01 \% \mathrm{CO}_{2},$ and the room has a volume of 2500 cubic feet.
(a) Find a differential equation satisfied by the amount $f(t)$ of $\mathrm{CO}_{2}$ in the room at time $t.$
(b) The model developed in part (a) ignores the $\mathrm{CO}_{2}$ produced by the respiration of the people in the room. Suppose that the people generate .08 cubic foot of $\mathrm{CO}_{2}$ per minute. Modify the differential equation in part (a) to take into account this additional source of $\mathrm{CO}_{2}.$

In the problem we have. But a. So here C. F T equals 0.01 In two, entities square plus 40-plus 64 to the power to upon three. Now we have to find CST There's equals to 0.01 into two upon 3 In 2, 0 point to the Esquire Plus 40 plus 64 to the power To a .3 -1 In two, and 2 to T plus four. So this is equal to 0.01 into 8/3 in 20 point to the esquire plus 40 plus 64 to the power minus one upon three into 0.1 T Plus one. So finally this is equal to 0.0267 in 20.2 T squared Plus 40 plus 64 To the power -1 upon three into 0.1 T plus one. So we have serious T equals this. Now we have further to find CS five. So see there's five in part B of the problem, they have. So in part B See there's five equals to 0.0267 into 0.2 into 25 Plus 20 plus 64. To the power -1 upon three into 0.5 plus one. Now, further this equals two 0.0267 into 89. To the power minus one A bond three into 1.5. And this is equal to 0.00897 triple zero. That corresponds to 0.0090 bpm. But here, so this is the answer to the problem.

So we know that we're dealing with formaldehyde, and we know that if the concentration is above 33 micrograms per cubic foot, that that's supposed to be a strong smell and irritating to the eyes. So anything higher than this is quote bad and we have a room in part A. We know that it is 10 ft by 10 ft by 8 ft ceilings. So our first question is how Maney, What's the volume of the room? So it's 18, 800 cubic feet, and we know that there's one panel that is a 4 ft by 8 ft panel. So ah, four by 8 ft panel that whips. And that's supposed to be feet of paneling that's put up. And we know that that paneling has one one square foot. Well, Imette, 3365 micrograms per day formaldehyde. And so we want to figure out how much formaldehyde is there and figure out how maney, how much it's gonna admit per day. And so we know that we have an air service area of 32 square feet and we know that one square foot William it 3365 micrograms per day. So when we multiply that out, we get 107,680 micrograms per day. That's what it will. He met that one piece of wood, so we want to write a function for that. That's part C for how much formaldehyde there would be in the room. And so will he met 1107 1006 180 times X If X is in days, and that's how much will be admitted. And then we want to know, How long is it going to take for it to end up basically burning our eyes? If we had that piece of paneling in there, and so we know that the this is in this is how much is there per day? And we know the volume is 800 cubic feet. So when we divide that, we get 134.6, and that's how maney micrograms there would be per cubic foot per day or cubic foot her day. And we know that in one day that's gonna be higher than 33. So this is per day. So what fraction of the day is going to take to be over. Well, if we take the, um 33 out of we want to know when does what X causes that to equal 33. And so what number causes that to be equal to 33. And if we take 33 divided by 134.6, we get approximately 0.25 days. So in a quarter of a day, which is about six hours, you would feel the burning effect from that formaldehyde if you had that much in that paneling.

So we want to let why to be equal to Y. Of C. Be the ramones of carbon mono outside which is ceo. That's a symbol in the room at time. T. That's I see so they amount therefore the amounts the moms of See you couple when I was like entering the room, entering their room is going to be for divided by 100 Times three over the same. And this is going to be 12 divided by housing beats QP minutes. And the amounts of carbon dioxide, the amounts of carbon you know outside of see you of ceo living live in their room, it's green to be white. So we have Why divided by 4500 Times three Divided by Time. And this will give us why Divided by 15,000 Fc QP minutes. So this implies that oh I do I. D. C. It's going to be 12 divided by housing minus Why divided by 15 1000. Which implies that the way the way D. T. Last one over you've seen 1000 it's equal to so divided by that. So we just have a change of subjects here. So from here this implies that our P. Of T. E. T. It's equal to well divided by 15,000. Then our cue See it's also equal to 12 divided by that was them. Okay, so then it's implies that our V. V. Of T. Is going to be E. To the power see Divided by 15 hours when. Okay. So to find why So you know the derivative. Well if you want to find where we have to integrate. So this implies that why is going to be one divided by E. C. The power Is the poet. See over 15 1000 named Segre of So over a 10 you have E To the power see over 15 house and D. T. And this is equal to why to D. T. So if you saw in place that's why it's going to be equal to mm to the power minus T. Divided by 15 1000 times two of times 15 divided by 1000. Yeah then you have E. Experience nine S. T. Divided by 15. That was when Liza constants C. So plus the constant C. See and this is equal to it's the power minus T. Divided by 15,000. We have 180 e. to the power C. divided by 15. How is you? Class? I can start to see so that's why not the initial to fairly you what we have it's its initial value we have why we have why notes. So this change way. No it's to be equal to zero which implies that we have zoo two Vehicle to one. You have 180 because any number is surprise Aries wants to have 1 80. Let's see. So this implies that our c. is equal to negative 180. So Therefore Ry is going to be equal to because now we know the value of that so it's going to be 180. My next 180 E. Exponent minus T. Divided by one self. You've seen how was name. So when the concentration we are seeing that swing when the concentration of C. You are carbon monoxide is 0.0 1% in the room in their room. Then it implies that the amounts the amounts of ceo satisfies why divided by 4500 which is equal to 0.01 divided by 100. And it's in place that our why here it's equal to zero points 45 feeds cute. And the other aspect it's let's see the room we are looking at contains the amounts so window so oh yeah I've seen this window, window room contents. This amounts these amounts a month Sweden. We have we have zero 0.45 To be equal to 180 -18 C. He said the par -T divided by 15,000. Which implies that I have 1 779.5 five divided by 18 C. Which is equal to E. To the power My Nestea divided by 15 1000 So two so 40. This implies that our c. Here it's equal to when it's 15,000 lane because you take lane of pace so lame off. 479.55 Divided by 1 80. And this is a quick violently equal to 37 0.55 may needs. So this is the time the time when the concentration of a carbon monoxide in the room riches zero points 0/1. Hence our final results for the time. It's texas solving points 55 minutes

Okay. One cute. Cute. Okay, we're see Cuba Year Teoh e u. The term in Q t Work Utd beat at 0.0 e with way 15,000 Their team B Teoh equal to these. Should you call the base 37 point, I mean it.


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