Thermostat - Replace Battery

Hi everyone,
I have a Mcquay Thermostat and this is my question. Recently my replace battery light on my thermostat came on, so I did the logical thing and replaced my batteries. The problem though is two minutes later it came back on. I thought that I would have to buy a new thermostat but then I realized that the "C" wire was hooked into it making this a dual powered thermostat. This means it runs off my battery or my electricity.

I was wondering was this always running off my electricity in the first place and the battery was a backup. If this is the case then I do not need to replace it. If it is not the case will this have a big effect on my electric bill if I continue to run it off my electricity instead of the battery?

Thanks for the help.
Yes, I have contacted Mcquay, but no one is in until Monday.

Thanks,

Not sure if powered by electricity, and if it is, it would not take much power.

Okay, thank you. I spoke with an electrician and he told me the batteries are just purely for backup in case of the loss of power. The idea is with the batteries there you won't lose the programming. Thanks for the help.