Are you sure you don't mean "county"? There are cities that define themselves as being in "the country", but in the United States, if you live outside of city limits, that's the county.
Solid Waste is an enterprise utility; like water, sewer, or power. If you have someone who picks up your trash, they either work for an independent contractor (Waste Management is a big one), and you pay them a monthly fee. Or it is an enterprise fund from your Municipality (if not a city, as in your case, the County); that is funded by fees they collect specifically for it, not taxes.
OT: http://www.ncsu.edu/ehs/www99/right/handsMan/lab/flam.html