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A tank contains 70 kg of salt and 2000 L of water. Water containing 0.4kg/L of...

A tank contains 70 kg of salt and 2000 L of water. Water containing 0.4kg/L of salt enters the tank at the rate 16L/min. The solution is mixed and drains from the tank at the rate 4L/min. A(t) is the amount of salt in the tank at time t measured in kilograms.
(a) A(0) =  (kg)
(b) A differential equation for the amount of salt in the tank is  =0=0. (Use t,A, A', A'', for your variables, not A(t), and move everything to the left hand side.)
(c) The integrating factor is
(d) A(t) =  (kg)
(e) Find the concentration of salt in the solution in the tank as time approaches infinity. (Assume your tank is large enough to hold all the solution.)
concentration =  kgL

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Pg 1 solution Initially tank contains 70 kyy Salt and 2000 L Alt is the amount salt in the tank at time t measured in erams.Rake lg 2 Notulo Liquid coming in, water containing 0.4 kg/L of salt is coming in the tank at the 16 L/min. 0.4kg /L* 16 L/ m193 Ikus our initial value problem is A = rate in -rate out det so imin 4A 2000 + lat, A 6.4 OA 1000 t 6t Goth salt where A194 Integrating factor (IF) at 1000 tot If = е. 1000+ 6t If e 2. ! ln 1000 + 6t IA 6 e 7 ln 1000 +67 1 If = e Answer If= (100to. A 13 (1000 to yo 70 = 0:8 (1000+ 0 tc 10x7o = 0.8 x 10000 tc C= 7300 A = (1000+ 6+ / A = 0.8/1080 t6 ) 3 - 4300 0.8 (1000

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