Diluting a solution A tank is filled with 100 L of a 40% alcoholsolution (by volume). You repeatedly perform the following operation:Remove 2 L of the solution from the tank and replace themwith 2 L of 10% alcohol solution.a. Let Cn be the concentration of the solution in the tank after thenth replacement, where C0 = 40%. Write the first five termsof the sequence {Cn}.b. After how many replacements does the alcohol concentrationreach 15%?c. Determine the limiting (steady-state) concentration of the solutionthat is approached after many replacements.
Diluting a solution A tank is filled with 100 L of a 40% alcoholsolution (by volume). You repeatedly perform the following operation:Remove 2 L of the solution from the tank and replace themwith 2 L of 10% alcohol solution.a. Let Cn be the concentration of the solution in the tank after thenth replacement, where C0 = 40%. Write the first five termsof the sequence {Cn}.b. After how many replacements does the alcohol concentrationreach 15%?c. Determine the limiting (steady-state) concentration of the solutionthat is approached after many replacements.
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Diluting a solution A tank is filled with 100 L of a 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.
a. Let Cn be the concentration of the solution in the tank after the
nth replacement, where C0 = 40%. Write the first five terms
of the sequence {Cn}.
b. After how many replacements does the alcohol concentration
reach 15%?
c. Determine the limiting (steady-state) concentration of the solution
that is approached after many replacements.
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