Do you think that the rate of carbon dioxide production during fermentation would be affected by the availability of simple sugars? Explain.

Yes. Simple sugars can enter the glycolytic pathway through feeder pathways. Eventually, this can lead to production of pyruvate. If there is no oxygen available, and the organism performs alcoholic fermentation, the more pyruvate available, the more CO2 that can be produced.  

(I am aware there are other fermentation pathways that make CO2)

If we were treating this reaction as a first order rate reaction, then rate = k[Pyruvate]^x  

This is a forward reaction, by LeChatlier's Principle, thermodynamically, more [pyruvate] would increase the amount of [CO2] and [EtOH].

In addition, the rate law shows increasing [Pyruvate] increases the rate of CO2 production, assuming that x > 0.

This means if the amount of sugar converted eventually into pyruvate per time is high, then the rate of CO2 production should be high.

Explanation:

cells spend most of their time in interphase