When a majority of the legislative body of a charter city determines that it would serve the best interests and general welfare of such city to become a charter code city, such legislative body may, by resolution, declare its intention to adopt for the city the classification of charter code city and to be governed under the provisions of this title, with the powers conferred hereby. Within ten days after the passage of the resolution, the legislative body shall cause it to be published at least once in a newspaper of general circulation within the city. Upon the expiration of the ninetieth day from, but excluding the date of first publication of the resolution, if no timely and sufficient referendum petition has been filed, as determined by RCW 35A.29.170, the intent expressed in such resolution shall be effected by passage of an ordinance adopting for the city the classification of charter code city.