It's hard to get an accurate count of the earth's population but there are a lot more than 3 billion people on earth right now. Probably around 7 billion. In 300+ years there will be closer to 10 billion people.
See my above posts on why that's unlikely. Heck, there's serious question about whether or not the Earth can sustain even a six-billion population.
Earth has sustained a population of six billion for several years now without difficulty.
No one starves on Earth anymore due to insufficient food being available. They starve for political reasons.
With Trek era technology (fusion and antimatter reactors, the ability to grow large amounts of food in space or import it from agricultural worlds, the ability to build urban areas underground and in the ocean.........) chances are Earth could support 20 or 30 billion with little difficulty.
Incidentally, IIRC, the FASA Federation sourcebook gives Earths 23rd century ere population at 22 billion.
Not canon of course, but as realistic as the "3 billion" given in this OP.
Dayton3, do you really want me to drag Christopher in here and have him prove you wrong on this issue again like in the "Star Charts" thread back in TrekLit? Heck, as he noted, the sheer heat generated by thirty billion people and the technological infrastructure needed to support that population would screw with the ecosystem too much for it all to be viable.