6. Suppose a 100-gallon tank is full of fresh water initially, with 5 gallons of salt water being pumped in every minute and 5 gallons of the mixture being removed. However, suppose that the system takes a while to clear residual fresh water out of the intake, so that the concentration of salt in the incoming water is 0.25(1 – e-t/5) lb/gal. Find a formula for A(t), the amount of salt in the water in the tank (in pounds) after t minutes.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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6. Suppose a 100-gallon tank is full of fresh water initially, with 5 gallons of salt water
being pumped in every minute and 5 gallons of the mixture being removed. However,
suppose that the system takes a while to clear residual fresh water out of the intake, so
that the concentration of salt in the incoming water is
0.25(1 – e-t/5) lb/gal.
Find a formula for A(t), the amount of salt in the water in the tank (in pounds) after t
minutes.
Transcribed Image Text:6. Suppose a 100-gallon tank is full of fresh water initially, with 5 gallons of salt water being pumped in every minute and 5 gallons of the mixture being removed. However, suppose that the system takes a while to clear residual fresh water out of the intake, so that the concentration of salt in the incoming water is 0.25(1 – e-t/5) lb/gal. Find a formula for A(t), the amount of salt in the water in the tank (in pounds) after t minutes.
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