Usually it is recommended to start tomato seeds 5 to 7 weeks before planting outside.

I started my 4th of July tomatoes early February, almost 5 weeks ago and they are about 4 inches tall. so if 2 inches per weeks is right, by May 1st they will be 18" tall!.

There are several reasons why i started early. I want tomatoes early in the season. Plus i am thinking to repot them to the second leaves so they have stronger roots and control the plant size.

So to answer your question, a 3 to 4 month plant will be about 4 to 9 feet tall depending on the type of plant, indetermine or determine. I am not so sure if you can grow them without fertilizer at all. They will need it. Good luck!