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.
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.
