Question

The air in a 75 cubic metre kitchen is initially clean, but when Laure burns her...

The air in a 75 cubic metre kitchen is initially clean, but when Laure burns her toast while making breakfast, smoke is mixed with the room's air at a rate of 0.04 mg per second. An air conditioning system exchanges the mixture of air and smoke with clean air at a rate of 4 cubic metres per minute. Assume that the pollutants are mixed uniformly throughout the room and that burnt toast is taken outside after 42 seconds. Let S(t) be the amount of smoke in mg in the room at time t (in seconds) after the toast first began to burn.

a. Find a differential equation obeyed by S(t).

b. Check that the solution is correct using S(12).

c. Check what is the level of pollution after 42 seconds, correct to 10 significant figures (do not incude units)

d. The time, in seconds, when the level of pollution falls to 0.004mg per cubic metre is ____________ seconds.

e. Find S(t) for 0≤t≤42 by solving the differential equation in (a) with an appropriate initial condition.

f.. What is the level of pollution in mg per cubic meter after 42 seconds?

g. How long does it take for the level of pollution to fall to 0.004 mg per cubic metre after the toast is taken outside?

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The air in a 69 cubic metre kitchen is initially clean, but when David burns his...
The air in a 69 cubic metre kitchen is initially clean, but when David burns his toast while making breakfast, smoke is mixed with the room's air at a rate of 0.08 mg per second. An air conditioning system exchanges the mixture of air and smoke with clean air at a rate of 9 cubic metres per minute. Assume that the pollutants are mixed uniformly throughout the room and that burnt toast is taken outside after 76 seconds. Let S(t)...
A 17000 cubic foot room initially has a radon level of 880 picocuries per cubic foot....
A 17000 cubic foot room initially has a radon level of 880 picocuries per cubic foot. A ventilation system is installed that brings in 400 cubic feet of air per hour that contains 3 picocuries per cubic foot, while an equal quantity of the well-mixed air in the room leaves the room each hour. Setup and use a differential equation to determine how long it will take for the room to reach a safe to breathe level of 120 picocuries...
History of Present illness: Mrs.Tomy, patient of Dr. Brents, has been admitted for removal of her...
History of Present illness: Mrs.Tomy, patient of Dr. Brents, has been admitted for removal of her gallbladder. She presented to the hospital with severe 10/10 epigastric pain that caused nausea and vomiting. She is now one day post-op cholecystectomy that was done laparoscopically.. The patient attributes poor control of her diabetes over the past 6 months to the increased stress of caring for her husband with little support. Social History: Lives with husband Henry, who has advancing dementia. They have...
Please answer the following Case analysis questions 1-How is New Balance performing compared to its primary...
Please answer the following Case analysis questions 1-How is New Balance performing compared to its primary rivals? How will the acquisition of Reebok by Adidas impact the structure of the athletic shoe industry? Is this likely to be favorable or unfavorable for New Balance? 2- What issues does New Balance management need to address? 3-What recommendations would you make to New Balance Management? What does New Balance need to do to continue to be successful? Should management continue to invest...