2. (LE-3) A tank is initially filled with 800 gallons of pure water. Brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 5 gallons per minute. The well-mixed solution is pumped out at the same rate. (a) Let A(t) be the amount of salt (in pounds) in the tank after t minutes. Write the equations for the initial value problem which would model A(t). (b) Solve for A(t) in the initial value problem you wrote in the previous part. (c) Approximate the time T, to the nearest hundredths place, in which the tank con- tains exactly 400 pounds of salt.
2. (LE-3) A tank is initially filled with 800 gallons of pure water. Brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 5 gallons per minute. The well-mixed solution is pumped out at the same rate. (a) Let A(t) be the amount of salt (in pounds) in the tank after t minutes. Write the equations for the initial value problem which would model A(t). (b) Solve for A(t) in the initial value problem you wrote in the previous part. (c) Approximate the time T, to the nearest hundredths place, in which the tank con- tains exactly 400 pounds of salt.
Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:2. (LE-3) A tank is initially filled with 800 gallons of pure water. Brine containing 4 pounds of salt per gallon is pumped into the tank at a rate of 5 gallons per minute. The well-mixed solution is pumped out at the same rate.
(a) Let \( A(t) \) be the amount of salt (in pounds) in the tank after \( t \) minutes. Write the equations for the initial value problem which would model \( A(t) \).
(b) Solve for \( A(t) \) in the initial value problem you wrote in the previous part.
(c) Approximate the time \( T \), to the nearest hundredths place, in which the tank contains exactly 400 pounds of salt.
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