Problem 2. A tank is filled with 100 L of 40% alcohol solution (by volume). You repeatedly perform the following operation: Remove 2 L of the solution from the tank and replace them with 2 L of 10% alcohol solution. 1. Let Cr be the concentration of the solution in the tank after the nth replace- ment, where Co = 40%. Write the first five terms of the sequence Cn. 2. After how many replacements does the alcohol concentration reach 15%? 3. Determine the limiting (steady-state) concentration of the solution that is ap- proached after many replacements.

Fig: 1