When was Model 722 Serial Number 43799 manufactured?

If you are asking about a Remington model 722 bolt action rifle?Then the letter code which can be found on the barrel will date your rifle for you.Get the 2,or 3 letter code and go to Remington arms Company and look up the letter code by year.

I don't think Remington Arms Company has it on their web but the Remington Society of America does, see related links.