A tank with 1000 liters of water initially contains 4 g of calcium.

Question

A tank with 1000 liters of water initially contains 4 g of calcium. Water with a concentration of 2 mg/L (milligrams/liter) is pumped into the tank at a rate of 1 L/min and the mixture is pumped out at the same rate.

(a) Write a differential equation and its initial condition for, y(t), the TOTAL amount of calcium in grams (not milligrams!) in the tank. (t is measured in minutes. Note: 1g = 1,000 mg).

(b) Find the general solution to this differential equation.

(c) Find the particular solution satisfying the initial condition.

(d) (i) Draw a sketch for all possible solutions to this differential equation and (ii) include a sketch (in bold) of the solution obtained in (c).

(e)

(i) What is the amount of calcium in the tank after 1/2 hour? (ii) According to the solution found in (c), what is the amount of calcium if we wait forever? Explain! Why?

Answer 1