Answer Happy

The air in a 71 cubic metre kitchen initially clean, but when Margaret burns her toast while making breakfast, smoke is mixed with the room's air at a rate of 0.05 mg per second. An air conditioning system exchanges the mixture of air and smoke with clean air at a rate of 6 cubic metres per minute. Assume that the pollutant is mixed uniformly throughout the room and that burnt toast is taken outside after 32 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. Find S(t) for 0 ≤ t ≤ 32 by solving the differential equation in (a) with an appropriate initial condition. c. What is the level of pollution in mg per cubic meter after 32 seconds? d. How long does it take for the level of pollution to fall to 0.003 mg per cubic metre after the toast is taken outside? You can confirm that you are on the right track by checking numerical answers to some parts ds(t) dt a. The differential equation is than just S.) (Enter your expression using Maple syntax and use S(t) rather mg (Enter your answer correct to at b. As a check that your solution is correct, test one value. S(13) = least 10 significant figures. Do not include units.) c. Check the level of pollution in mg per cubic metre after 32 seconds by entering your answer here, correct to at least 10 significant figures (do not -3 include the units): mg m d. The time, in seconds, when the level of pollution falls to 0.003 mg per cubic metre is seconds (correct to at least 10 significant figures). Note that this check asks for the time since t = 0 but the question part (d) asks for a time since the toast was taken outside.