The director of environmental management may, in his or her discretion, establish circumscribed areas within which all bovine cattle are subjected to the tuberculin test, but in no case shall that area be smaller than a single city or town as provided. Before this area is established, the owners of eighty-five percent (85%) of the cattle, or seventy-five percent (75%) of the cattle owners in this area shall make application, in writing, on official form to the director, placing their herds under the inspection and supervision of the state or of the United States, for the eradication of bovine tuberculosis. Upon receipt of a sufficient number of those applications, the director shall first satisfy himself or herself that those applications have been signed by the requisite number of cattle owners within the designated area, and all those applications are open to inspection at all times. If satisfied that those applications have been signed by the requisite number of cattle owners, the director may establish this area or areas which he or she shall clearly bound and describe, and within which bovine tuberculosis is to be eradicated at the expense of the state or United States, and he or she shall cause all those cattle within that area or areas to be quarantined, tested, appraised, and condemned as provided in § 4-5-1 — § 4-5-6.