Your fuel injector computer will readjust itself, too, over a period of several days. This is normal. Never pay full price for a battery. Remember, a battery with a small capacity will be under high stress all the time. There are many different quality ranges of battery usually expressed in terms of months of life.
Many batteries fail prematurely, especially in hot, humid environments.
If your battery lasts its full warranty life that's rare, and you can expect it to be on its last legs. Generally, don't be surprised if your battery fails any time after its first two years of in-car use. Buy only batteries of the proper capacity for your car, and only when they are are on sale. Many times sale batteries are far better values than top of the line batteries. In general, try to find a battery with a warranted life of about 30 months.