Question

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.)

Answer 1

`Q(3\,min) = 0.349\,pd`

Explanation:

The expression for the salt in the barrel is:

`Q(t) = 6\cdot (1-e^(-0.02\cdot t))`

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

`Q(3\,min) = 6\cdot [1-e^(-0.02\cdot (3\,min))]`

`Q(3\,min) = 0.349\,pd`