Dynamic by default
Your provider assigns addresses from a pool with a lease, much as a router does inside your home. The lease is renewed while you stay connected and released when you do not, so the address can go to another subscriber.
In practice it changes when your router reboots or loses connection for long enough, when the provider performs maintenance, and on some networks at a fixed interval regardless. Fibre and cable connections often hold the same address for months; older DSL lines were commonly cycled every night.
Why providers do it
IPv4 addresses are scarce and now genuinely expensive to acquire, and a provider with more subscribers than addresses can only work if the addresses circulate. Dynamic assignment is the mechanism.
There is a second, older reason: a rotating address discourages people from running servers on a residential line, which is what the residential price is predicated on. This is also why residential ranges appear on policy-based mail blocklists — a description of the range, not an accusation about you.
When a static address is worth it
You want one if you are hosting something that has to be reachable at a stable address, running a mail server, or on the other end of a firewall rule somebody else maintains. Providers usually sell it as an add-on, often only on a business plan.
For everything else — including reaching your home network from elsewhere — dynamic DNS is the cheaper answer: a small client tells a DNS provider your current address whenever it changes, and you use a name instead.
Watching it change
The history page on this site records the addresses your browser has arrived on and when each first appeared. That record lives in your own browser's storage and is never uploaded — a log of one person's addresses over time is exactly the kind of record we are not interested in keeping.