If you want your population to grow, you need high morale.
morale "boosters" are: make sure you have enough residences (shows <100% demand); your food supply is growing, and NO structures "Disabled" in the morale report (eg, nursery, university or gorf).
Also make sure your med.center demand is <100%.
One important rule i found: if a certain tech is not 100% required yet - don't get it (if it can create a morale-problem, like a gorf or med.centers). As long you don't
research medical centers or gorf, your population doesn't demand any; and it wont effect your morale. First make sure you have enough scientists/workers to actually fill those medical centers, before doing the reseacrh.
I know some other players would disagree, but i found it to work well for the earlier missions.
Oh, one more thing: high levels of unemployment also effects morale rather dramaticly. To solve this: what i do is create a couple of ore storage tanks, since they aren't too expensive, and usually won't cause much problems in case some (or even all) get idled/disable/destroyed, BUT: it can keep workers busy - morale can go up, and birth rates along with it. And remember: no new workers if ya have no children :rolleyes:
Good luck, and welcome to the club!
