Whenever any city of the second class decreases in population until it has a population of less than eight hundred inhabitants and more than one hundred inhabitants, as determined by the most recent federal decennial census or the most recent revised certified count by the United States Bureau of the Census, the mayor and city council may decide by ordinance to remain a city of the second class. If the mayor and city council enact such an ordinance, the mayor shall certify such fact to the Secretary of State who, upon the filing of such a certificate, shall by proclamation declare such city to remain a city of the second class. Such city shall continue to be governed by laws of this state applicable to cities of the second class.