(a) In the event the governing body shall determine that the management and control of said hospital shall be vested in a board of trustees, said governing body shall appoint five (5) trustees. Said trustees shall be residents of the city but no more than one physician shall be appointed.

(b) At any time subsequent to the initial appointment of a five (5) member board of trustees, the governing body by resolution may increase the number of trustees to serve on the board to seven (7) or nine (9) members. In the event the governing body does not increase by resolution the number of members to serve on the board of trustees, said board of trustees shall consist of five (5) members.

(c) The members of the first board shall be appointed one for a term of one (1) year, one for a term of two (2) years, one for a term of three (3) years and two for a term of four (4) years, and upon the expiration of the terms of those originally appointed their successors shall be appointed for terms of four (4) years. In case of a vacancy a successor shall be appointed for the unexpired term.

(d) Whenever the number of members of an existing board of trustees is increased by resolution of the governing body, said governing body shall provide by resolution for the expiration of the terms of the members appointed to the new positions on the board of trustees to coincide with the expiration of the terms of the members serving on the board of trustees at the time of the creation of said new positions so that no more than a simple majority of the members of said board of trustees is appointed at the same time. Upon the expiration of the terms of those originally appointed pursuant to this subsection (d) their successors shall be appointed for terms of four (4) years.