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'78 isn't old enough for exemption:
Q: Who is required to have their vehicle emissions tested?
A: All residents of the greater Phoenix and Tucson areas and those who regularly commute into the areas for work or school are required to have their 1967 or newer vehicles pass an emissions test. Most vehicles newer than 6 years old are exempt from testing, and certain other vehicle exemptions apply (see Exemptions). If you are not sure if you live in the emissions control area, CLICK HERE.
Full info for you:
https://www.myazcar.com/home