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Mixture - Math 17B Kouba Mixture Problems EXAMPLE 1 Let S...

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Unformatted text preview: Math 17B Kouba Mixture Problems EXAMPLE 1 : Let S represent the amount (in pounds) of salt in a tank at time t minutes. A solution containing 2 lbs. of salt per gallon flows into a tank at the rate of 3 gal. / min. and the well—stirred mixture flows out of the tank at the same rate. The tank initially holds 500 gallons of solution containing 25 lbs. of salt. a.) Set up a differential equation with initial conditions representing the rate of change of salt in the tank. Solve the equation. b.) How much salt is in the tank after 10 minutes ? after 1 hour ? c.) How much salt do you expect to be in the tank as It gets infinitely large ? EXAMPLE 2 : Let S represent the amount (in pounds) of salt in a tank at time t minutes. A solution containing 2 lbs. of salt per gallon flows into a tank at the rate of 3 gal. / min. and the well—stirred mixture flows out of the tank at the rate of 5 gal. /min. The tank initially holds 500 gallons of solution containing 25 lbs. of salt. a.) How many gallons of solution are in the tank after 1 minute ? after 10 minutes ? after 50 minutes ? after t minutes ? When will the tank be empty ? b.) Set up a differential equation with initial conditions representing the rate of change of salt in the tank. Solve the equation. 0.) How much salt is in the tank after 10 minutes ? after 100 minutes ? after 200 minutes ? after 240 minutes ? d.) What will be the maximum of salt in the tank and at What time will it occur ? ...
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