Carrillo Knight
11/03/2023 · Middle School

A graphing device is recommended. A 60 -gallon barrel is filled completely with pure water. Salt water with a concentration of \( 0.3 \mathrm{lb} / \mathrm{gal} \) is then resulting mixture overflows at the same rate. The amount of salt in the barrel at time \( t \) is given by \[ Q(t)=18\left(1-\mathrm{e}^{-0.07 t}\right) \] where \( t \) is measured in minutes and \( Q(t) \) is measured in pounds. (a) How much salt (in lb) is in the barrel after 9 minutes? (Round your answer to two decimal places.) (b) How much salt (in lb) is in the barrel after 18 minutes? (Round your answer to two decimal places.)

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(a) After 9 minutes, there is approximately 8.46 pounds of salt in the barrel. (b) After 18 minutes, there is approximately 12.93 pounds of salt in the barrel.

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