23F09-methods

# 23F09-methods - minutes 2 Determine the basic principle to...

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Math 3323 Fall 2009 Text, p. 60: 4 A tank with a capacity of 500 gal originally contains 200 gal of water with 100 lb of salt in solution. Water containing 1 lb of salt per gallon is entering at a rate of 3 gal/min and the mixture is allowed to flow out of the tank at a rate of 2 gal/min. Find the amount of salt in the tank at any time prior to the instant when the solution begins to overflow. Find the concentration (in pounds per gallon) of salt in the tank when it is on the point of overflowing. Compare this concentration with the theoretical limiting concentration if the tank had infinite capacity. 1. Define variables. Let Q(t) = the amount (in pounds) of salt in the tank at time t (in
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Unformatted text preview: minutes). 2. Determine the basic principle to be used. The rate of change of the amount of salt in the tank is equal to the rate at which salt is entering minus the rate at which salt is exiting. Mathematically, 3. Write down the differential equation that describes the situation. (entering concentration) (entering flow rate) (exiting concentration) (exiting flow rate) dQ dt In this problem, 4. Now determine the initial condition. 5. We now have a first-order linear initial value problem. (We should be getting to the point where we eat these for breakfast!)...
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