A Library Board of Trustees consisting of five (5) members shall be appointed by a vote of the Mayor and entire Council, as provided in section 304(b) to serve without compensation. The Mayor and entire Council may remove Trustees in the same manner. The Board shall:
a. Be responsible for providing adequate library services;
b. Appoint a Library Director;
c. Administer the Library budget allocated by the Council;
d. Make and enforce all rules and regulations applicable to library services; and
e. Administer such additional matters as may be determined by ordinance.