Question

Ch2.3- Applications of First Order Linear Equations: Previous Problem Problem List Next Problem (1 point) A tank contains 1400 L of pure water. Solution that contains 0.04 kg of sugar per liter enters the tank at the rate 7 L/min, and is thoroughly mixed into it. The new solution drains out of the tank at the same rate. (a) How much sugar is in the tank at the begining? y(0) = 0 (kg) (b) Find the amount of sugar after t minutes. y(t) = (kg) (c) Ast becomes large, what value is y(t) approaching? In other words, calculate the following limit. lim y(t) = (kg)

Answer 1

Pule Water soltim that Com teins A temk Cemtainj 1400L ate Limin dSugasper liter enters the tomk al the omd ig mixed mto it The new soution drains oud dthe tenk at the Same Yale much sugs i^ in the temk af the beginin So the tamk Star ling pale Water So Find 4 sugah after tminutes the amonl

let yt) 3 mass sugoh imk in the temk at time t minules The rake the soukm emtening He tomle egual t £eaving thetemt the voume t the solutien isSemne im the taE neglechvj Veick'vmaemsitz _ Yafe LImin dyar m 004 kglL m d menchewge imsugeh Gemtry dy) dt mean Smmall time inesv 200 200 AP 200dyt) 200 dy 20ody 56- P 200 1P m Lo t side m rati y the 200 R-25 n s-ytCio - 200 -200 ln 156 c C vlueSusH s he im eguation () -200 ml 56-9l - t-200n56 200 n156-1 +20cm/56 t

200 n 200 In 200 - t 200 APPy Anilog both side 56 S I-e g(e) 56 C1-e So) lim 56 (-e200 ). gE) 56 C1-E) YCa)56 C-0) 56kg 56 k