The city is prohibited from changing from the mayor-council form of government within two years after the adoption thereof. At the end of such period, or at any time thereafter, the city's form of government may be amended or changed when:
(1) A written petition executed by 10 percent of the number of those who voted in the last city election is submitted to the council with the proposed changes or amendments incorporated in the petition; after presentation of the petition, the council shall call for a referendum vote on the proposed changes and amendments, and
(2) A majority of the votes cast in the referendum is in favor of the proposed changes or amendments. After the council receives the proposed changes and petition, it shall call a special election for the purpose of determining whether the city shall adopt the changes or amendments. Notice shall be given of the time and purpose of such election by publication once each week for four consecutive weeks in a newspaper published in said city prior to the referendum vote. All qualified electors of such city may participate in the election and such questions shall be plainly printed upon the ballot. The referendum shall be conducted, the expenses paid, the votes canvassed and the results declared in the same manner as is provided by law in other city elections.