The board is given the following powers and duties:

(1) To provide for the collection of all moneys provided for in this chapter;

(2) To provide for payment of all annuities and benefits under this chapter;

(3) To provide for and maintain all necessary administrative facilities and personnel;

(4) To provide for payment of all administrative salaries, fees, and expenses;

(5) To hear and determine applications for membership in this fund according to the terms of this chapter;

(6) To hear and determine applications for retirement, disability, and death benefits according to the terms of this chapter;

(7) To make rules, regulations, and requirements consistent with this chapter for determining eligibility of members for disability, death, and retirement benefits;

(8) To delegate its authority to invest funds to one or more members of the board;

(9) To provide for the keeping of minutes and records of all meetings and proceedings of the board, including all rules, regulations, delegations, and requirements passed upon by the board;

(10) To delegate any and all duties and authorities granted in this Code section to the secretary-treasurer under such conditions as may be deemed proper by the board, provided that the board shall at all times hear and determine any matter arising under this chapter if it so desires, if such matter is referred to it by the secretary-treasurer, or if such matter is appealed to the board by any person affected by a decision made by the secretary-treasurer;

(11) To exercise such other powers, not inconsistent with this chapter, as are necessary for the proper administration of this chapter; and

(12) To correct errors in the records of the fund in those instances in which an error results in a member or beneficiary receiving more or less than he or she would have been entitled to receive had the records been correct and to adjust the payments, as far as is practicable, in such a manner that the member or beneficiary is paid the actuarial equivalent of the benefit to which he or she is actually entitled.