Hi there. To test whether your alternator is definitely failing, do this; get the car started, either via a jump start or a charged -up battery and then switch on all the electrics you can find i.e. full headlights, heater blower, rear demister, interior lights, etc. and leave a good long while like this. Then try to notice if there is any considerable and continuous dimming of any lights taking place. If there is, your alternator is on the way out. If not, you have a faulty discharging battery and your alternator is fine.