how to do last two blanks TextHath Drawing Plot Animation Hide eck Most of your marks are assigned to your wntten presentation C Mapie Irout 10.4-10.4 exp (-13/520) ▼ | | Courier New The air in a 52 cubic metre kitchen is initially clean, but when Alex burns his toast while making breakfast, smoke is mixed with the room's air at a rate of 0.02 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 pollutants are mixed uniformly throughout the room and that burnt toast is taken outside after 31 seconds. Let S() be the amount of smoke in mg in the room at time (in seconds) atter the toast first began to 0.4-10.4e evalf [10] (8) 0.25677692 a. Find a differential equation obeyed by S(t) b. Find S(t) for Ost 31 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 31 seconds? d. 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? 10.4-10.4 exp (-31/520) 520 10.4 10.4e > evalf [10] () 0.601881068 >-520 1n ((0.004-10.4)/(-10.4)) You can confirm that you are on the right track by checking numerical answers to some parts BN .As a check that your solution is correct, test one value. $(13) 25677692 0.2000384794 dS(t) aThe differentia equation is _- 002-Sty520 (Enter your expression using Maple (Enter your express on using Maple syntax) (Enter your answer corect to 10 significant figures) c. Check the level of pollution after 31 seconds by entering your answer here, correct to 10 significant figures (do not include the units) 601881068 d. The time, in seconds, when the level of pollution falls to 0.004 ng per cubic metre is seconds Note that this check asks for the time since t 0but the question part (d) asks for a time since the toast was taken outsidc. TextHath Drawing Plot Animation Hide eck Most of your marks are assigned to your wntten presentation C Mapie Irout 10.4-10.4 exp (-13/520) ▼ | | Courier New The air in a 52 cubic metre kitchen is initially clean, but when Alex burns his toast while making breakfast, smoke is mixed with the room's air at a rate of 0.02 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 pollutants are mixed uniformly throughout the room and that burnt toast is taken outside after 31 seconds. Let S() be the amount of smoke in mg in the room at time (in seconds) atter the toast first began to 0.4-10.4e evalf [10] (8) 0.25677692 a. Find a differential equation obeyed by S(t) b. Find S(t) for Ost 31 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 31 seconds? d. 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? 10.4-10.4 exp (-31/520) 520 10.4 10.4e > evalf [10] () 0.601881068 >-520 1n ((0.004-10.4)/(-10.4)) You can confirm that you are on the right track by checking numerical answers to some parts BN .As a check that your solution is correct, test one value. $(13) 25677692 0.2000384794 dS(t) aThe differentia equation is _- 002-Sty520 (Enter your expression using Maple (Enter your express on using Maple syntax) (Enter your answer corect to 10 significant figures) c. Check the level of pollution after 31 seconds by entering your answer here, correct to 10 significant figures (do not include the units) 601881068 d. The time, in seconds, when the level of pollution falls to 0.004 ng per cubic metre is seconds Note that this check asks for the time since t 0but the question part (d) asks for a time since the toast was taken outsidc.