The board of county commissioners shall appoint three (3) qualified county residents as members of the central Utah district board of health. They shall each serve terms of five (5) years and their qualifications shall be in compliance with the provisions of the Utah health act as found in Utah Code Annotated section 26A-1-109; provided, however, that if one of the appointed members is appointed by virtue of his membership on the board of county commissioners, he shall serve at the pleasure of the county commissioners. (1988 Code § 7.01.050)