Question

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) be the amount of smoke in mg in the room at time  t (in seconds) after the toast first began to burn. How long does it take for the level of pollution to fall to 0.002 mg per cubic metre after the toast is taken outside?

Please notice the time is after the toast is taken outside. Thanks for your help.

Answer 1