Can’t tell until some testing is done. If this is the original battery, suspect that battery is probably the problem. It may be at the end of its useful life.
I would charge it overnight and then drive to a place like Advance Auto, where they can test the battery and alternator for free, in most states. Call ahead to make sure you aren’t wasting the trip.
Given the age of the battery, you could also buy a battery (Costco appears to have best prices and best warranty these days), install it, and then go get the alternator checked to make sure you don’t also have an alternator problem. If you don’t want to do that, using a place that installs batteries (Advance Auto, Walmart, Sears, etc) would be your better option. Walmart may not do on-car alternator testing, though.
Some of this testing can be done at home if you have a volt meter and can measure the charge coming to the battery. It will tell you whether the alternator output is OK or not.