What time period did the Mochica live in?

Mochica did not "live." Mochica is the extinct pre-columbian language of northwest Peru. By the beginning of the 20th century it was spoken in only a few villages of the Chiclayo region of northern Peru. It was first documented in 1607 by Fernando de la Carrera in his Arte de La Lengva Yvnga de Los Valles del Obispado de Truxillo del Peru, con vn Confessonario, y todas las Oraciones Christianas, traducidas en la lengua, y otras cosaspublished in 1644 (Lima) but has not been spoken as a language since the 1920's and the last loan Words seem to have fallen out of usage by 1960.