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.