You don't give any details of your system, or what is running in the background, but that type of behaviour is not unusual, especially with a dial-up connection.
Gone are the days of 'simple' web sites. Nowadays they are full of content and that dial-up connection is going to be busy.
My question is about the Double Computer Icon in my Systems Tray. It is continuosly sending and receiving bytes even when I am not working in a site. Is this normal? They never go black.
I have HP Home and am on dial-up.