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A 500 gallon tank is filled with fresh water in which 80 pounds of salt are dissolved. Fresh water is flowing into the tank at a rate of 2 gallons per minute and a saline solution with a concentration of 0.8 pounds of salt per gallon is flowing into the tank at a rate of 3 gallons per minute. The well mixed solution in the tank drains at a rate of 5 gallons per minute. Let Q be the amount of salt, in pounds (Ibs), in the solution aftert minutes (min) have elapsed. a. Draw a diagram that represents this situation, then setup a differential equation with an initial condition that describes the rate of change in the amount of salt in the tank. b. Draw a phase line for this differential equation and describe the behavior of the equilibrium solutions. What does the amount of salt in this tank approach after a long time (write answer using limit notation)? c. Solve this differential equation and determine the amount of time it takes to get within 3% of the equilibrium amount.

A 500 gallon tank is filled with fresh water in which 80 pounds of salt are dissolved. Fresh water is flowing into the tank at a rate of 2 gallons per minute and a saline solution with a concentration of 0.8 pounds of salt per gallon is flowing into the tank at a rate of 3 gallons per minute. The well mixed solution in the tank drains at a rate of 5 gallons per minute. Let Q be the amount of salt, in pounds (Ibs), in the solution aftert minutes (min) have elapsed. a. Draw a diagram that represents this situation, then setup a differential equation with an initial condition that describes the rate of change in the amount of salt in the tank. b. Draw a phase line for this differential equation and describe the behavior of the equilibrium solutions. What does the amount of salt in this tank approach after a long time (write answer using limit notation)? c. Solve this differential equation and determine the amount of time it takes to get within 3% of the equilibrium amount.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter2: Equations And Inequalities
Section2.7: More On Inequalities
Problem 44E
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A 500 gallon tank is filled with fresh water in which 80 pounds of salt are dissolved. Fresh water is flowing into the tank at a rate of 2 gallons per minute and a saline solution with a concentration of 0.8 pounds of salt per gallon is flowing into the tank at a rate of 3 gallons per minute.. The well mixed solution in the tank drains at a rate of 5 gallons per minute. Let Q be the amount of salt, in pounds (Ibs), in the solution after t minutes (min) have elapsed. a. Draw a diagram that represents this situation, then setup a differential equation with an initial condition that describes the rate of change in the amount of salt in the tank. b. Draw a phase line for this differential equation and describe the behavior of the equilibrium solutions. What does the amount of salt in this tank approach after a long time (write answer using limit notation)? c. Solve this differential equation and determine the amount of time it takes get within 3% of the equilibrium amount.
Transcribed Image Text:A 500 gallon tank is filled with fresh water in which 80 pounds of salt are dissolved. Fresh water is flowing into the tank at a rate of 2 gallons per minute and a saline solution with a concentration of 0.8 pounds of salt per gallon is flowing into the tank at a rate of 3 gallons per minute.. The well mixed solution in the tank drains at a rate of 5 gallons per minute. Let Q be the amount of salt, in pounds (Ibs), in the solution after t minutes (min) have elapsed. a. Draw a diagram that represents this situation, then setup a differential equation with an initial condition that describes the rate of change in the amount of salt in the tank. b. Draw a phase line for this differential equation and describe the behavior of the equilibrium solutions. What does the amount of salt in this tank approach after a long time (write answer using limit notation)? c. Solve this differential equation and determine the amount of time it takes get within 3% of the equilibrium amount.
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