All the officers in any such city, elected or appointed under the provisions of the former act of incorporation of such city, and in office at the time of such reincorporation under this act, shall continue to exercise their respective functions under the provisions of this act of reincorporation for the full term for which they were so elected or appointed, and until their successors shall have qualified and entered upon the duties of their office, unless herein otherwise provided.
MCL 113.3