Chapter 4.2, Problem 82E

Concentration of a Mixture A 1000-liter tank contains 50 liters of a $$25\%$$brine solution. You add $x$liters of a $$75\%$$brine solution to the tank.

(a) Show that the concentration $C$, the proportion of brine to total solution, in the final mixture is $C=\frac{3x+50}{4(x+50)}$.

(b) Determine the domain of the function based on the physical constraints of the problem.

(c) Sketch the graph of the concentration function.

(d) As the tank is filled, what happens to the rate at which the concentration of brine is

increasing? What percent does the concentration of brine appear to approach?