Most likely. After three or four days, you won't have that much population growth. You need more RAMZ.
Sims wont use more than 2gig of RAM anyway.
As for system specs, my Wife's computer is much the same spec and the only lag she seems to have is a mild graphical lag in larger houses. On the other hand, I have a PC that's over twice as powerful in almost every regard, but seem to suffer more lag than her, with far less items. However, I do have a town with around 300 sims in it (including service npc)