associating task with account for service dept

I'm trying to figure out how tasks fit into the picture here. I have a service dept that creates a service item, lets say some sort of problem at a customer's home that i need to dispatch a tech to.

So I create a task and then schedule this task basically just using the calendar date function. The task is associated with a contact, but if I pull up the account, I don't see the task (only the service item). The task dropdown has the account option in it, so I can change a task to an account (odd) but I can't assign a task to an account.

I may just be using the system wrong, so any pointers would be greatly appreciated. Thanks!