All regulations within this chapter shall apply to lands located in Winnebago County which are within two miles of the City as shown on the Official Zoning Map of the City. The exemption from regulation granted by Section 414.23, Code of Iowa, to property used for agricultural purposes shall apply to said unincorporated area. The specific regulations and districts hereunder shall be terminated within three months of the establishment of the administrative authority for County zoning, or at such date as mutually agreed upon by the City and County.