(h) An additional county or counties may be added to an existing Authority if a petition of five per cent (5%) of the qualified voters is filed with and an election is called by the Commissioners Court of the county or counties seeking admission to an Authority. If the vote is favorable, then admission may be granted to such county or counties by the Board of Directors of the then existing Authority upon such terms and conditions as they may agree upon and evidenced by a resolution approved by two-thirds (2/3rds) of the then existing Board of Directors. The county or counties that may be so added to the then existing Authority shall be given representation on the Board of Directors by adding additional directors in proportion to their population according to the last preceding Federal Census.