If your ISP uses DHCP rather than a fixed address which a lot do, then about all they can tell is the ISP you use. Unless you pay for a fixed IP address, most ISPs prefer DHCP to their modems since for example if you go on vacation the address might go to someone else during your absence if the modem is turned off.
From :
Computer Forensics: Tracking an Offender | Internet Fundamentals | InformIT
"IP address can be statically or dynamically assigned. Computers that are assigned a static IP address always use the same IP address until it is manually changed to a new address, which is becoming increasingly less convenient in a time of constant reorganizations and mobile computers. Dynamic addresses are automatically assigned to a computer when it registers itself on a network using a protocol called Dynamic Host Configuration Protocol (DHCP) or Windows Internet Naming Service (WINS), a Microsoft protocol that is rapidly becoming obsolete. For network administrators, DHCP neatly solves the tedium and confusion of manually assigning constantly moving Internet devices. Virtually all ISPs use DHCP to assign addresses to their dial-up customers, and many permanently connected home users have dynamically assigned addresses that can change whenever their cable modems are powered off and on. Use of DHCP is definitely on the increase, but unfortunately, DHCP makes detective work a little more difficult."
AS noted if you power off your modem for a while or the power goes out you may get a new IP address. (If your behind a router you may also use a local dhcp server on the in home network, which may have an IP address of 192.168.1.x (of which there are likley millions of boxes with each address as the router converts these local addresses to routeable addresses thru something called NAT. This is partly why the old IPv4 still works a lot of devices sit behind routers/firewalls that do the conversion. If you have more than one device connected to the internet you likley use local dhcp as well.