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A tank initially contains so lb of salt dissolved in 400 gal of water, where so is some positive number. Starting at time t=0, water containing 1.5 lb of salt per gallon enters the tank at a rate of 6 gal/min, and the well-stirred solution leaves the tank at the same rate. Letting c(t) be the concentration of salt in the tank. t time t, show that the limiting concentration that is, lim c(t)-is 1.5 lb/gal. Write an equation for the rate of salt (in lb/min) that flows into the tank, where t is the time in minutes.

A tank initially contains so lb of salt dissolved in 400 gal of water, where so is some positive number. Starting at time t=0, water containing 1.5 lb of salt per gallon enters the tank at a rate of 6 gal/min, and the well-stirred solution leaves the tank at the same rate. Letting c(t) be the concentration of salt in the tank. t time t, show that the limiting concentration that is, lim c(t)-is 1.5 lb/gal. Write an equation for the rate of salt (in lb/min) that flows into the tank, where t is the time in minutes.

Advanced Engineering Mathematics
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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A tank initially contains so lb of salt dissolved in 400 gal of water, where so is some positive number. Starting at time t = 0, water containing 1.5 lb of salt per gallon enters the tank at a rate of 6 gal/min, and the well-stirred solution leaves the tank at the same rate. Letting c(t) be the concentration of salt in the tank at time t, show that the limiting concentration that is, lim c(t)—is 1.5 lb/gal. t→∞ Write an equation for the rate of salt (in lb/min) that flows into the tank, where t is the time in minutes. Flowin =
Transcribed Image Text:A tank initially contains so lb of salt dissolved in 400 gal of water, where so is some positive number. Starting at time t = 0, water containing 1.5 lb of salt per gallon enters the tank at a rate of 6 gal/min, and the well-stirred solution leaves the tank at the same rate. Letting c(t) be the concentration of salt in the tank at time t, show that the limiting concentration that is, lim c(t)—is 1.5 lb/gal. t→∞ Write an equation for the rate of salt (in lb/min) that flows into the tank, where t is the time in minutes. Flowin =
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