The term of the 5 persons to be appointed by the Mayor shall be three (3) years except that the term of two (2) of the members appointed to the first Board shall be for only one (1) year, and the term of two (2) members of the first Board shall be for two (2) years. In the event that a vacancy shall occur during the term of any member, his or her successor shall be appointed for the unexpired portion of the term.