Question

can anyone solve for question part d

The air in a 48 cubic metre kitchen is initially clean, but when David buns his toast while making breakfast, smoke is mixed with the rooms ar at a rate of 0.08 mg conditioning system exchanges the mixture of air and smoke with clean air at a rate of 5 cubic metres per minute. Assume that the polutants are mioxed uniformly throughout the room and that burnt toast is taken outside after 75 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 bun per second An ar a. Find a differential equation obeyed by S(t) b. Find S(t) for O St s 75 by solving the differential equation in (a) with an appropriate initial condition. c, what is the level of pollution in mg per cubic meter amer 75 seconds? d. 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? You can confirm that you are on the right track by checking numerical answers to some parts dS(t) (Enter your expression using Maple syntax) a. The differential equation is b. As a check that your solution is correct, test one value. S(19)1.495203945 c Check the level of pollution after 75 seconds by entering your answer here corect to 10 signiticant figures (do (Enter your answer correct to 10 significant figures.) not indude the units): 0.1172039871 mg m ih seconds Note hat this check tls or th ks for the tim d. The time, in seconds, when the level of pollution falls to 0.002 mg per cubic metre is 48.84922459 since t -O but the question part (d) asks for a time since the toast was taken outside

Answer 1

dluhone a iuen that volume al kitchenE eubic metere the air conditionern is Se exahangtna the mixtwa af air and am oke with clean ir at a dak op S cubs metas ber minute nol the bwrnt toast us takent ouide altes of ano Ct) s ths arnount tr the toasti began to bun H given Lonalihons re 다 dも Kate at cohich smake and air is exehanyi dlt mixed in th cluan air of smoke in ai exch = 0.08-( amount al smoke in aporm volume d(Ut).。.og mg / gee 81t) ー olt

dt $76 46.08- e $26 r10 llns t/ will be sayo on

1957 s76 46 08-C (C forts secj (75 volu me . 9138 128 4 8 (dy INe hatu iwe haine to ud the tine urhen &(t) 0.00 此/s% 0-00 208 -0.99子916 0:997916 0.00 38440401-t- t=1.64 seconds

Please thumbs up if it was helpful will be glad to know.