A tank contains 30 lb of salt dissolved in 500 gations of water. A brine solution is pumped into the tank at a rate of 5 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 5 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by (t)-2+ sin(t/4) lb/gal. A(C)-1000+ 250 +359(sin (4)-25 con())- 313 x Without actually graphing, conjecture what the solution curve of the IVP should look like. Then use a graphing utility to plot the graph of the solution on the interval [0, 300) A A 1000 800 600 400 200 t 50 100 150 200 250 300 2000 1500 1000 500 50 100 130 200 250 - 300
A tank contains 30 lb of salt dissolved in 500 gations of water. A brine solution is pumped into the tank at a rate of 5 gal/min; it mixes with the solution there, and then the mixture is pumped out at a rate of 5 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by (t)-2+ sin(t/4) lb/gal. A(C)-1000+ 250 +359(sin (4)-25 con())- 313 x Without actually graphing, conjecture what the solution curve of the IVP should look like. Then use a graphing utility to plot the graph of the solution on the interval [0, 300) A A 1000 800 600 400 200 t 50 100 150 200 250 300 2000 1500 1000 500 50 100 130 200 250 - 300
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 contains 30 lb of salt dissolved in 500 gallons of water. A brine solution is pumped into the tank at a rate of 5 gal/min; it mixes with the solution there, and then the
mixture is pumped out at a rate of 5 gal/min. Determine A(t), the amount of salt in the tank at time t, if the concentration of salt in the inflow is variable and given by
(C) 2+ sin(t/4) lb/gal.
(9)-
x
Without actually graphing, conjecture what the solution curve of the IVP should look like. Then use a graphing utility to plot the graph of the solution on the interval [0, 300)
A
A(0) 1000+
A
1000
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250
313
50 100 150 200 250
-950e
300
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t
300
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