Writeup:
Preturn - The settler took 6 turns, growth was in 10. Did you waste 4 turns by not building the settler?

A spearman could have been built in that time, or even 2 warriors (future Immortals).
The worker is building a road in Persepolis's borders (desert).

First, there's plains that offer more food. Second, it's best to connect the other city. A road should have been built east of the wheat. (3 total tiles).
Good choice on not using the worker as a conlony. Culture borders will eventually absorb it. It's also best to have 2 workers build roads on the same tile (complete in 1 turn on grasslands, plains, desert, tundra).
Micromanagement - I'd like to see more on this (what you did in the game). For instance, "Persepolis grew to size 3, placed worked tile from desert to roaded plains).
Turn 10 - Persepolis set to build archer.
Our Ultimate Unit is the Immortal. We should be building warriors, as they upgrade to Immortals. We also need to be building barracks once we have 6-8 cities - not to mention workers). I also suggest building a granary in Persepolis.