A 50-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 pounds/gallon is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt (in pounds) in the barrel at time t (in minutes) is given by Q (t) = 15 (1 - e-kt) where k > 0.

Find k if there are 8.5 pounds of salt in the barrel after 20 minutes. Solve for k exactly and then give your answer to 4 decimal places.

Question

Deanna

Mathematics

20 March, 13:36

A 50-gallon barrel is filled completely with pure water. Salt water with a concentration of 0.3 pounds/gallon is then pumped into the barrel, and the resulting mixture overflows at the same rate. The amount of salt (in pounds) in the barrel at time t (in minutes) is given by Q (t) = 15 (1 - e-kt) where k > 0.

Find k if there are 8.5 pounds of salt in the barrel after 20 minutes. Solve for k exactly and then give your answer to 4 decimal places.

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Answers (1)

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Deangelo Rivera · Answer 1

The equation for determining the value of Q (t) is,

Q (t) = 15 x (1 - e^-kt)

Directly substitute to this equation the values given,

8.5 lbs = 15 x (1 - e^ (-k) (20))

The value of k and the answer to this item is approximately equal to 0.0418.