Halving the alveolar ventilation will double the PACO2. However, halving the alveolar ventilation will MORE THAN halve the PAO2. I have been playing around with the aveolar gas equation for the past couple of hours and have even searched for a a mathematical explanation of this using the equations, but have not had any luck. I think the fact that there is another variable to add (FIO2) in the alveolar air equation that is really confusing me (whereas is the alveolar ventilation equation all the variables are multiplied or divided and not added or subtracted) and preventing me from seeing this relationship between a change in "V dot A" and PAO2. I don't know if I explained that clearly.

I am trying to come up with a general relationship that says if I multiply alveolar ventilation by "x", I will cause a change in PAO2 by more than x or less than x.

Maybe I am missing something really simple here, but I couldn't figure it out even after a couple of hours...Any one have a good handle of this concept and is wiling to share their understanding? Any help would be very much appreciated,