Answer Happy

yct) = y Problem Three (10 pts): A tank contains 1000L of pure water. Brine that contains .05 kg of salt per liter of water enters the tank at a rate of 5L/min. Brine that contains .04 kg of salt per liter of water enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L/min. For the differential equation y(0)=100002 dy - by(t), y(0) = 40 dt YLE where r and b are constants determined by the parameters of the problem described above: 1. (3pts) In terms of r and b, find the general solution to this differential equation. dy dy (r-bldt y dy 4+) += 2. (3pts) In terms of r, b, and yo, find the particular solution for the given initial condition. dt =r-byct) =(r-b) dt ... ) Ing=(r=b)t + c ya ecrable cupyt)= ct = rt tbt HC 10 000 = e 10 000 e yoo-100002 ro-bo 2000 tc 10000) - IC C 9999 y(t)= e AC ortabt 10ood = etc +9999 3. (2pts) Find r, b, and yo in terms of the problem parameters given above. dy_5 l/min - 5 l/mindo.sk LHey 4. (2pts) In terms of r and b, find lime--y(t).