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Unformatted text preview: Math 334 Lecture #5 § 2.3: Modeling with First Order ODE’s A Tank Mixing Problem. There is a pond containing 10 millions gallons of fresh water. Water flows into the pond at a rate of 5 million gallons per year, and water flows out of the pond at 5 million gallons per year. After a point in time (say t = 0), a chemical with a concentration 2 + sin(2 t ) grams per gallons accompanies the water flowing into the pond. [Sketch picture of this situation.] Let Q ( t ) be the amount of chemical (in grams) in the pond at time t (in years). The principle that governs this situation is rate of change of chemical in pond is equal to the rate at which the chemical flows into the pond minus the rate at which the chemical flows out of the pond. In terms of the variables Q and t , this principle is dQ dt = rate in- rate out , where the rate in is the water inflow rate times the concentration of the chemical in the inflow stream, 5 × 10 6 gallon year · ( 2 + sin(2 t ) ) gram gallon = 5 × 10 6 ( 2 + sin(2...
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This note was uploaded on 03/08/2011 for the course MATH 334 taught by Professor Smith during the Spring '11 term at Vanderbilt.
- Spring '11