A50-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.