It will but it doesn't change as often, when I was a Cox Cable Internet customer my IP remain the same for months until I started to change routers. If you are worry about it changing you can sign up for the free dynamic dns service like No-IP - Dynamic DNS, Static DNS for Your Dynamic IP. What this service does is give you a static URL that is easy to remember like brock-no-ip.com, then you configure your router dynamic DNS feature with the information like user name, password and the host "no-ip.com" and whenever your IP changes this information will be updated on their server.