: a very large tank initially contains 15 gallons of saltwater Recall the salty tank containing 6 pounds of salt. Saltwater containing 1 pound of salt per gallon is pumped into the top of the tank at a rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. Let's call this salty tank from class Tank A. Consider the following modifications: • Tank B is the same basic scenario as Tank A, but pure water is being pumped into Tank B instead of saltwater. • Tank C is the same basic scenario as Tank A, but the rates are switched: saltwater enters Tank C at a rate of 1 gallon per minute, and leaves at a rate of 2 gallons per minute. (a) Set up and solve initial value problems that correspond to individual Tanks B and C. (b) Use a plot to compare the three solution curves (including the solution for Tank A) and discuss how these curves predict or represent outcomes you would expect from the description of each scenario.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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9. Recall the salty tank
containing 6 pounds of salt. Saltwater containing 1 pound of salt per gallon is pumped into the top of the
tank at a rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of
1 gallon per minute. Let's call this salty tank from class Tank A. Consider the following modifications:
: a very large tank initially contains 15 gallons of saltwater
• Tank B is the same basic scenario as Tank A, but pure water is being pumped into Tank B instead of
saltwater.
• Tank C is the same basic scenario as Tank A, but the rates are switched: saltwater enters Tank C at a
rate of 1 gallon per minute, and leaves at a rate of 2 gallons per minute.
(a) Set up and solve initial value problems that correspond to individual Tanks B and C.
(b) Use a plot to compare the three solution curves (including the solution for Tank A) and discuss how
these curves predict or represent outcomes you would expect from the description of each scenario.
Transcribed Image Text:9. Recall the salty tank containing 6 pounds of salt. Saltwater containing 1 pound of salt per gallon is pumped into the top of the tank at a rate of 2 gallons per minute, while a well-mixed solution leaves the bottom of the tank at a rate of 1 gallon per minute. Let's call this salty tank from class Tank A. Consider the following modifications: : a very large tank initially contains 15 gallons of saltwater • Tank B is the same basic scenario as Tank A, but pure water is being pumped into Tank B instead of saltwater. • Tank C is the same basic scenario as Tank A, but the rates are switched: saltwater enters Tank C at a rate of 1 gallon per minute, and leaves at a rate of 2 gallons per minute. (a) Set up and solve initial value problems that correspond to individual Tanks B and C. (b) Use a plot to compare the three solution curves (including the solution for Tank A) and discuss how these curves predict or represent outcomes you would expect from the description of each scenario.
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