The following problem deals with the open three-tank system. Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rate r gallons per minute. The initial amounts x1(0)= x0 (lb), x2(0) = 0, and x3(0) = 0 of salt in the three tanks are given, as are their volumes V1, V2, and V3 (in gallons). First solve for the amounts of salt in the three tanks at time t , then determine the maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x1 (t) , x2(t) , and x3(t).r = 30, x0 = 27, V1 = 30, V2 = 15, V3 =10

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Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 18T

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The following problem deals with the open three-tank system. Fresh water flows into tank 1; mixed brine flows from tank 1 into tank 2, from tank 2 into tank 3, and out of tank 3; all at the given flow rate r gallons per minute. The initial amounts x₁(0)= x₀ (lb), x₂(0) = 0, and x₃(0) = 0 of salt in the three tanks are given, as are their volumes V₁, V₂, and V₃ (in gallons). First solve for the amounts of salt in the three tanks at time t , then determine the maximal amount of salt that tank 3 ever contains. Finally, construct a figure showing the graphs of x1 (t) , x2(t) , and x3(t).

r = 30, x₀ = 27, V₁ = 30, V₂ = 15, V₃ =10

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