Although population growth rates are falling, the population size has actually remained to be increasing. This is due to the exponential rate of size increasement which occurs as the size of the population gets larger. This can be easily demonstrated using a number sequence. If we assume a constant population growth rate of 2X, the number sequence is: 1 - 2 - 4 - 8 - 16 - 32 - 64 - 128 - ...

In practice a population increase by 2X means that a (monogamous) couple (hence consisting of 2 people) would have 4 children (we hence assume that the parents die over time). A population growth rate of 1X would mean 2 children in practice. A sustainable population number is estimated by many environmental organisation at about 2 billion people.[1] Although this number is discutable, there is a general concensus the population number should be (allot) lower than what it is now (7 billion people). As such, in practice, this would mean that would mean that the population size should be falling (which isn't the case now, at all, see the table at this wikipedia article) and the amount of children per (monogamous) couple should be 2 or less (ie 1 child). This, as the population growth rate needs to become 1X or less than 1X. If we assume a 1X population rate (2 children) starting at the population size we currently attained (7 billion, but let's assume 8 for convenience), the sequence would be: 1 - 2 - 4 - 8 - 8 - ...

If we assume a 0,75X population rate (1,5 children[2]) starting at the population size we currently attained (7 billion, but let's assume 8 for convenience), the sequence would be: 1 - 2 - 4 - 8 - 6 - 4,5 - ...

If we assume a 0,5X population rate (1 child) starting at the population size we currently attained (7 billion, but let's assume 8 for convenience), the sequence would be: 1 - 2 - 4 - 8 - 4 - ...

## Notes

• It should be noted that even with 2 or 1 child per couple, the population size will actually be larger than what we like it to be (2 billion people) for a rather long time (40-60 years). This, as people live to an age of 70-80 years, and have their children at an age of 20-30 years.
• It should also be noted that the initial number of the population we use (7 billion) also includes the elderly and so the actual number that will actually reproduce at some point in the future (young people, ie 0 - 40 years old) will be smaller, so the population growth will be slightly smaller than what we anticipate (say 15%, see http://en.wikipedia.org/wiki/Demographics_of_the_world#Age_structure ).
• In the intrest of ecology, it can be argued that lower population growth rates should actually be attained in areas where there is less infrastructure, housing, ... and more in more urbanized areas. This, so that less extra urbanization needs to be performed in pristine areas (ie areas that have not have their original vegetation (ie forests, ...) removed and are still rich in biodiversity). In practice this means that population growth rates would need to be higher for many developed countries and lower for many developing countries. This however can be perceived as discriminitive to some and is thus a more or less controversial idea.