Doug,
I don't have my e-smith test box up and running anymore, but somewhere in the /etc directory (/etc/dhcpc/ on my Red Hat box) will be a file that contains the DHCP information. There should be a line in a file that says something like RENEWALTIME. The number associated with this tag is in seconds and tells you how often your IP gets renewed. You should also see dhcpcd messages in /var/log/messages (I think).
On a side note:
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I have been using Rogers@Home for a couple of years now, and my IP address hasn't changed. The address does get renewed twice a week. This means I can get away with using regular DNS.
Keep in mind that I keep the machine on all the time. If you leave your machine off for a couple of weeks, the assigned IP address will likely change (it depends on how Rogers configured their DHCP servers).
Cheers,
Peter.