Disclaimer: I am not a demographer, I just play one on TV.
It's fun to play around with the numbers, but one must also take into account that pregnancy and birth is very taxing on the body. So most people don't want to bear more children than they have to. By that I mean to overcome mortality rates.
Prior to the Industrial Revolution, average fertility rates were in the region of 6 children per woman -- but, on average, 4 of those 6 died before having children of their own. With the Industrial Revolution living conditions improved, leading to lower child mortality. As the mortality went down, so fertility followed -- albeit with a lag, so that in the 1960s there were 5 children born per woman, out of whom 4 survived.
Today, the average fertility rate is about 2.33 globally, and it keeps falling. (The ideal fertility rate for a stable population is of course 2.0, with zero child mortality, where two parents have two children who survive to replace them.)
Now, the Houses are all descended from high-tech, developed nations, which today have very low fertility rates. On the other hand, after the Exodus they had gone through a long period of war and were trying to establish colonies with a limited starting pop, which should drive fertility up.
Assuming that the Sleeper ships carried 30k people, as @Unseelie and @Kazinsal said, I put in these parameters:
Starting population: 30K
Immigration/year: 0
First birth given (age): 25
Human age (average): 80
Age pyramid: Flat
I chose a Total Fertility Rate of 3, which gave me a Yearly Growth Rate of 1.46%. After 800 years, the total population is 5.94 billion, and in 825 A.S. it's at 8.77 billion.
However, it is reasonable to assume that fertility would decline as the total population increased. It may be high initially, out of necessity, but it can then decline out of convenience.
So let's say that we start with a fertility rate of 4 for the first century. People are shagging like mad to build up a workforce, although they still want to be reasonably comfortable. After 100 years with a yearly growth rate of 2.42%, population has risen to 275'000 people.
For the second century, fertility drops to 3, yearly growth drops to 1.46%, and the population reaches 1 million in 201 A.S.
In the third through seventh centuries (still assuming no immigration), fertility drops to 2.5 and growth drops to 0.81%. In 701 A.S. the pop reaches 64 million.
In the final 125 years, fertility declines further to 2.1. Growth drops to 0.18%. In 800 A.S. the population is 74.35 million, and in 825/826 it'll hit 78 million.
Conclusion:
I think you can fudge the numbers any which way you want, really. You can have people have even more babies initially, and starting at a younger age. But I think it is important that fertility declines and the age of first birth increases over time. I still think the billions-upon-billions-upon-billions populations are a tad exaggerated.