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A graphing calculator is recommended.

A 20-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 lb/gal is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt in the barrel at time t is given by Q(t) = 6(1 − e−0.02t) where t is measured in minutes and Q(t) is measured in pounds.

How much salt is in the barrel after 3 min? (Round your answer to two decimal places.)

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xero099

Answer:

[tex]Q(3\,min) = 0.349\,pd[/tex]

Step-by-step explanation:

The expression for the salt in the barrel is:

[tex]Q(t) = 6\cdot (1-e^{-0.02\cdot t})[/tex]

The quantity of salt in the barrel after 3 minutes is:

[tex]Q(3\,min) = 6\cdot [1-e^{-0.02\cdot (3\,min)}][/tex]

[tex]Q(3\,min) = 0.349\,pd[/tex]

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