While the screen shots illustrate that it can be done, they don't explain the how.
How it's done depends on a lot of things, but there are several ways to manipulate population growth and loyalty.
1. The use of taxes can raise or lower both growth and loyalty. A change of one level of taxes, changes growth by 0.5% and loyalty by 20%. So if you want to encourage growth, lower taxes. Conversely, to slow growth, raise taxes. You may have to add garrison or a high influence governor (influence contributes to population loyalty) to keep loyalty above rebellion if you raise taxes. The Romans get an additional benefit from coliseums to raise happiness, but it does cost 400 denarii to hold monthly games. There is an excellent discussion in the Ludus Magna concerning the effect of garrison.
2. Temple choice plays a part in ZPG, but using a law & order temple (for those factions that have them) isn't always necessary. In the above Brutii campaign, Thermon, Larissa, and Croton all have the Mars Temple, Corinth has the Artemis Temple, and Sparta has the original Nike Temple it had when I captured it. Distance to capital, and culture penalties play a large part in determining which temples to use. The greater the distance-to-capital & culture penalties, the more important it is to use a law & order temple.
3. A general rule-of-thumb that I use is: if the population is <1000, use low taxes, build a fertility temple (if available), and do not train units from that city until a population of 2k is reached. Between 2k and 6k, I like to see the population growing at a 2 or 3% rate. This enables you to have the time to build most of the structures you can build for that city before the next level of governing building is required. Between 6k and 12k, I like to see growth at 1.5-2% for the same reasons just mentioned. At around 20k, some cities will slow to 0.5% growth. If it's a city that I wish to see reach 24k, then I build the highest level of farming available, and add things like sewers and public baths (all of which encourage growth). If I still cannot reach 24k, but am only a few hundred short, I'll ship in peasants from another city and disband them to reach the 24k. Also, this is where a governor with growth traits, or growth ancillaries come in handy.
In any case, there is no 1...2...3... method to it. There are a lot a variables including faction, temple selection, distance-to-capital, culture penalty, garrison, and many others. But you have ways to manipulate things your way. Use every single one of them!
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