After a complete application for an entertainment permit has been filed, the City Manager shall cause an investigation to be made of such application, and after such investigation has been completed, shall cause the application to be set for hearing before him or her and shall notify the applicant of the date of such hearing. The investigation, public hearing and approval or denial of the application shall be completed within forty-five (45) days of the filing of a complete application. The time limit set forth herein may be extended upon written authorization of the applicant.