The spelling of the word "rastogi" is determined by its pronunciation. According to IPA phonetic transcription, the first syllable is pronounced as /rɑːs/ with an "r" sound followed by a long "ah" sound. The second syllable is pronounced as /toʊg/ with a long "o" sound and a hard "g" sound. The final syllable is pronounced as /i/ with a long "e" sound. Therefore, "rastogi" is spelled with an "r", followed by "a", "s", "t", "o", "g", and "i."