The Authority shall be made up of five persons. The initial members of the Authority shall be appointed by the Mayor with the approval of the City Council. The terms of office of the initial members shall be for one year, two years, three years, four years, and five years, as designated by the Mayor. As the terms of the initial members expire, the City Manager shall appoint or reappoint the members with the approval of the City Council for five-year terms, unless a vacancy is being filled, in which case the appointment shall be for the remainder of the term of the member being replaced. There shall be no limit on the number of terms for which a member can be reappointed. Three members shall constitute a quorum for the transaction of business.