Each authority shall be governed by a board of directors. All powers of the authority shall be exercised by the board or pursuant to its authorization. The board shall consist of any number of directors, not less than three, who shall be elected by the governing body of the city for staggered terms as hereinafter provided. At the time of the election of the first board, the governing body of the city shall divide the directors into three groups containing as nearly equal whole numbers as may be possible. The governing body of the city shall specify for which term each director is elected. The initial term of office of the first group shall be two years each. The initial terms of office of the second group shall be four years each. The initial term of office of the third group shall be six years. Thereafter, the term of office of each such director shall be six years. If at the expiration of any term of office of any director, a successor thereto shall not have been elected, then the director whose term of office shall have expired shall continue to hold office until his successor shall be so elected. If at any time there should be a vacancy on the board, a successor director to serve for the unexpired term applicable to such vacancy shall be elected by the governing body of the city. Each director must be a duly qualified elector of the city. Directors shall be eligible for reelection. Each director shall be reimbursed for expenses actually incurred by him in and about the performance of his duties. Any director of the authority may be impeached and removed from office in the same manner and on the same grounds provided in Section 175 of the Constitution of Alabama and the general laws of the state for impeachment and removal of the officers mentioned in Section 175.