Depends on your cable ISP and how they have their DHCP ranges configured.
I'm on Cox, and they have such a large space configured that my IP has NEVER changed. They set their scavenge time pretty high, so even though my lease expires, I'll get the same one later.
My lease runs one day. I've left my PC off for a week during vacation, and got the same IP. I've also put in a different card (which causes a new IP because DHCP leases are tied to MAC addresses), and put the old one back several months later. Got the old IP again.
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