In: Math
Let m > 0 be a constant. Suppose a tank starts with 10kg of salt water with 1% salt by mass. Suppose further that every hour, m kg of salt water with a concentration of 10% salt is added, and 2kg of the water in the tank is drained. The solution is kept well mixed at all times.
(a) (2 points) Write a differential equation that describes the amount of salt in the water.
(b) (5 points) How long does it take for the water to reach 5%
concentration if m = 3.
(c) (5 points) Give a (simplified) equation describing a value for m
such that the solution to reaches exactly 5% concentration in
exactly 1 hour.