math modeling

Question


  1. Consider the following blood CO2/Ventilation system model:

            Cn+1 = Cn – bVn +m   and   Vn+1 = aCn   (constants a>0, b>0, m>0, 4ab<1),

Where Cn is the amount of CO2 in the blood and Vn is the volume fraction of a breath entering the blood by this CO2 during the nth breath. The – bVn term represents the amount of CO2 lost during the breath.

Prove that as n tends to infinity, Cn tends to a constant. What is that constant?

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