A tank initially contains 100 liters of pure water. A brine solution con- taining 2 kilograms of salt per liter enters the tank at the rate of 5 liters per minute. Concurrently, the mixture is well-stirred inside the tank and exits through an outlet valve at the rate of 5 liters per minute. Let y(t) be the amount of salt inside the tank at any time t≥ 0. Show that y(t) = 200(1-exp(-t/20)), for all t≥ 0.
A tank initially contains 100 liters of pure water. A brine solution con- taining 2 kilograms of salt per liter enters the tank at the rate of 5 liters per minute. Concurrently, the mixture is well-stirred inside the tank and exits through an outlet valve at the rate of 5 liters per minute. Let y(t) be the amount of salt inside the tank at any time t≥ 0. Show that y(t) = 200(1-exp(-t/20)), for all t≥ 0.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:A tank initially contains 100 liters of pure water. A brine solution con-
taining 2 kilograms of salt per liter enters the tank at the rate of 5 liters
per minute. Concurrently, the mixture is well-stirred inside the tank and
exits through an outlet valve at the rate of 5 liters per minute. Let y(t)
be the amount of salt inside the tank at any time t≥ 0.
Show that y(t) = 200(1-exp(-t/20)), for all t≥ 0.
1 11
n (0 del TL
14
A
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