Gary,
Most bull elk reach antler maturity at 6-8 years of age. A 340 Bull is a nice trophy, especially on public ground. I think most biologists would agree that with good genetics, food and 6-8 years to grow, most bull elk will reach 340 or more.
Here is a chart to help you score a Typical American (Rocky Mountain) Elk......
http://www.boone-crockett.org/bgRecords/bc_scoring_typicalelk.asp?area=bgRecords&type=Typical+American+Elk

Antler points usually go as follows: (western count)

1 1/2 years old- Spike
2 1/2 years old- 4-5 point
3 1/2 years old- small 6 point
4 1/2 year and older- 6 point or better

This is a basic rule of thumb, of course it varies with genetics but it holds true most of the time. I would guess a 340 bull would be 5-6 years old on average. Hope this helps.

Carl

That's a nice chart and it holds pretty true. Though I've seen some whale tail 5 pointers that were huge, that had to be in their prime.