On the first Monday in October in each year the board of county commissioners shall meet at the time and place designated in the notice, whereat any taxpayer may appear and be heard for or against any part of the budget. The hearing may be continued from day to day until concluded but not to exceed a total of five days. The officials in charge of the several offices, departments, services, and institutions shall, at the time the estimates for their respective offices, departments, services or institutions are under consideration be called in and appear before such hearing by the board at the request of any taxpayer and may be questioned concerning such estimates by the commissioners or any taxpayer present.