Why does the iPhone battery die so fast? What can be done?

My mother’s iPhone loses battery very quickly! Maybe… 1 hr – 1 hr 30 mins. It just dies so fast. She’ll not touch it at all during that time and yet it will still die! She used to be able to not charge it for 3 days straight (she’s not a very heavy user) but now in an hour or so’s time it’ll drain so fast. It’s the first model that came out. Hopefully one of you can help me help her. Thanks in advance!