SOLUTION: A tank contains 80 kg of salt and 1000 L of water. A solution of a concentration 0.04 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from

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Question 1184079: A tank contains 80 kg of salt and 1000 L of water. A solution of a concentration 0.04 kg of salt per liter enters a tank at the rate 8 L/min. The solution is mixed and drains from the tank at the same rate.
a.) What is the concentration of our solution in the tank initially?
concentration = 80/1000 (kg/L), correct
b.) Find the amount of salt in the tank after 4.5 hours.
amount = 149.3126623 (kg), wrong
c.) Find the concentration of salt in the solution in the tank as time approaches infinity.
concentration = 0.04 (kg/L), correct
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!

b.) The differential equation is
dQ%2Fdt+=+0.32+-+Q%2F125,

where Q is the amount of salt in the solution in kg, after time t.

The solution to this D.E. is Q%28t%29+=+40+%2B+40%2Ae%5E%28-t%2F125%29. After 4.5 hours, or t = 270 minutes,
Q%28270%29+=+40+%2B+40%2Ae%5E%28-270%2F125%29+=+red%2844.613%29 kg.