Within 60 days after corporate authorities of a single municipality qualified as an Authority under the provisions of Section 11-48.3-3 of this Division shall adopt a resolution or ordinance providing for an Authority, the mayor, with the advice and consent of the corporate authorities, shall appoint 3 members of the Board for an initial term expiring the second June first after appointment, 3 members of the Board for an initial term expiring the third June first after appointment, and 3 members of the Board for an initial term expiring the fifth June first after appointment, and until their successors have been appointed and qualified. At the expiration of the term of any member, the mayor with the advice and consent of the corporate authorities, shall appoint his or her successor in like manner for a term of 5 years from the first day of June of the year in which they are appointed, except in case of an appointment to fill a vacancy.
     The Board of an Authority comprised of combinations of municipalities, as provided in Section 11-48.3-3 of this Division, shall be appointed in the following manner: memberships for the Board shall be apportioned among the member municipalities, as nearly as possible, according to the proportion each municipality’s population as determined by the most recent federal census bears to the total population of the metropolitan area as determined by the most recent federal census. The initial terms of such appointees for each such municipality shall then be determined by lot. Each such mayor, with the advice and consent of his or her respective corporate authorities, shall then appoint the members allotted to him or her in the manner provided in this Section.
     Within 30 days after certification of his or her appointment, and before entering upon the duties of office, each member of the Board shall take and subscribe the constitutional oath of office and file it in the office of the Secretary of State.