Some games do population growth right. Take Civilization, for example. A single play-through can take over 24 hours. That might be a short time for some games or a long time for others, real-time games for instance.
Civilization can do population growth well because it's scope is so large. It is an entire planet over thousands of years. And, because it is a turn-based game. The turns in Civilization vary in length. In the beginning of the game, the turns are hundreds of years long but layer they can be less than a year long. This is because, as time goes on, it takes less time to accomplish the same amount of work or, in this case, population growth.
That works fine for tun-based games because everything is just an aggregation of things from the real world and time scales can vary.
That doesn't work for real-time games, however, since the game must be played in the lifetime of the player, not over thousands of actual years. One solution to this problem is to keep the population constrained as a part of the story. In Homeworld, the population was put onto the Mothership by the Bishop ships and it was plausible that your entire population for the entire game consists of that initial population.
Other games, like Fragmented Galaxy, can't use that option. I'm trying to make a fun game and a plausible simulation. This means trade-offs, unfortunately. In real life, the world population grows by about 10,000 per hour (0.000000014% growth). If a player invests an hour of time into my game I want them to have accomplished more than that.
In the interest of fun, I am considering a few options. Read about them in part 3.