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At the hummingbird food factory, hot water containing 1/3 of a pound of sugar per gallon of liquid is poured into a giant mixing tank at a rate of 6 gallons per minute. The tank, which initially contains a priming solution of 5 pounds of sugar dissolved in 11 gallons of water, is kept well-mixed and that well-mixed solution leaves the tank at a rate of 7 gallons per minute. Set up, but do not solve, an initial value problem (i.e., a rate of change equation with an initial condition) that models the amount of sugar in the tank as a function of time.

At the hummingbird food factory, hot water containing 1/3 of a pound of sugar per gallon of liquid is poured into a giant mixing tank at a rate of 6 gallons per minute. The tank, which initially contains a priming solution of 5 pounds of sugar dissolved in 11 gallons of water, is kept well-mixed and that well-mixed solution leaves the tank at a rate of 7 gallons per minute. Set up, but do not solve, an initial value problem (i.e., a rate of change equation with an initial condition) that models the amount of sugar in the tank as a function of time.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section: Chapter Questions
Problem 5T
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At the hummingbird food factory, hot water containing 1/3 of a pound of sugar per gallon of liquid is poured into a giant mixing tank at a rate of 6 gallons per minute. The tank, which initially contains a priming solution of 5 pounds of sugar dissolved in 1l gallons of water, is kept well-mixed and that well-mixed solution leaves the tank at a rate of 7 gallons per minute. Set up, but do not solve, an initial value problem (i.e., a rate of change equation with an initial condition) that models the amount of sugar in the tank as a function of time. Reach 1: Point out exactly where the assumption that the liquid in the tank is kept well-mixed is reflected in your equation above. Explain briefly. Reach 2: After 10 minutes, a change occurs in the situation described above: a leak develops in the tank, resulting in an additional 1 gallon of well-mixed solution leaving the tank each minute. At the same time, a source of pure water is added to the tank, at a rate of 2 gallons per minute. All else remains the same. Use a different variable to represent the amount of sugar in this "new" leaky tank, and let t = 0 correspond to the time the leak started. Write down an initial value problem corresponding to the amount of sugar in the new leaky tank. (Note: you do not need to solve the original problem in order to do this part.)
Transcribed Image Text:At the hummingbird food factory, hot water containing 1/3 of a pound of sugar per gallon of liquid is poured into a giant mixing tank at a rate of 6 gallons per minute. The tank, which initially contains a priming solution of 5 pounds of sugar dissolved in 1l gallons of water, is kept well-mixed and that well-mixed solution leaves the tank at a rate of 7 gallons per minute. Set up, but do not solve, an initial value problem (i.e., a rate of change equation with an initial condition) that models the amount of sugar in the tank as a function of time. Reach 1: Point out exactly where the assumption that the liquid in the tank is kept well-mixed is reflected in your equation above. Explain briefly. Reach 2: After 10 minutes, a change occurs in the situation described above: a leak develops in the tank, resulting in an additional 1 gallon of well-mixed solution leaving the tank each minute. At the same time, a source of pure water is added to the tank, at a rate of 2 gallons per minute. All else remains the same. Use a different variable to represent the amount of sugar in this "new" leaky tank, and let t = 0 correspond to the time the leak started. Write down an initial value problem corresponding to the amount of sugar in the new leaky tank. (Note: you do not need to solve the original problem in order to do this part.)
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