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Unformatted text preview: Monday, January 31 Lecture 12 : Problems involving differential equations (Refers to Section 9.3 and 9.4 in your text) Expectations: 1. Set-up differentiable equations in various problems and solve them. 2. Models for population growth. 12.1 Example Suppose a tank contains 1000 L of pure water. We are given the following facts: - Brine that contains 0.05 kg of salt per liter of water enters the tank at a rate of 5 L/min. - Brine that contains 0.04 kg of salt per liter of water enters the tank at a rate of 10 L/min. - The solution is kept thoroughly mixed and drains from the tank at a rate of 15 L /min. a) How much salt is in the tank after t minutes? b) How much salt is in the tank if the process is allowed to continue indefinitely? c) Confirm your answer in part b) by sketching a direction field for the DE. Solution: Let y ( t ) be the amount of salt in the tank after t minutes....
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