The board of county commissioners of any county having a population of more than ten thousand (10,000) and less than fifteen thousand (15,000) and having an assessed valuation of not less than forty-five million dollars ($45,000,000), may by resolution, and shall, upon presentation of a petition signed by ten percent (10%) of the qualified electors of such county determined upon the basis of the total vote cast for the secretary of state at the last preceding general election, cause to be submitted to the voters of such county at the first local or general election thereafter, or if the petition so requires, at a special election called for that purpose, the question of the establishment of a steam and oil museum and cultural center by such county.