The board of supervisors shall, at the meeting at which the order declaring the district to be organized is made, appoint a board of five directors to administer the affairs of the district. No person shall, at any time, be eligible to hold the office of director of any district unless he or she is a resident of the state, and a cottongrower, either individually or as a joint tenant of, or is a member of a partnership which owns, or is an officer of, a corporation which grows cotton within the district.