Iv'e got a LG MP3 Player, with 32built in memory. Bought in 2003

I've recently upgraded from 128mb to 256mb SD Memory card which is the maximum for this little player.

But with this, my battery life time usage has considerably decreased. I'm using Duracell Plus. [PS. This mp3 player didn't come with a rechargeable battery]

So does the increase in memory increase battery usage exponentionaly?