It took from the beginning of time until 1850 for the world's population to reach 1 billion. By 1900, it had doubled, by 1930, it had reached 3 billion, sometime in the 1960's, 4 billion, 1980's, 5 billion, and today we're over 6 billion. Curiously, the Industrial Revolution was in full swing in Europe and North America in 1850; the rising standard of living initally increased population. However, as industrialization in a particular country continued, births declined, due to the shift from an agrarian to industrial economy; manpower began to be replaced by machinery. Right now, the two most populous countries on Earth, China and India, together have over half the population of the world. Both these giants are finally beginning to industrialize; as they do so, their population will eventually decrease. Within 200 years, we should be at a sustainable level, which may be around 2 to 3 billion. So the population graph, which loped along until 1850, has spiked from then until now, will most likely continue to spike for a time (50 years?) then should slide down and level out over the next 150.
Although the human population has been growing rapidly for the last 200 years (sort of a j-curve), this rate of growth does not seem ideal. Luckily, it also seems unlikely to continue.
I say it's not ideal because at that rate of growth we might reach carrying capacity and then start to have real problems with people dying as the planet can't sustain them all (of course, people like Malthus thought this was going to happen way back and it hasn't yet).
But the reason it's not likely is because the world is getting richer and people in richer "post-industrial" countries tend to have lower birth rates. I was just reading an article in "The Economist" that says that half the world lives in countries where the growth rate is less than "replacement" -- so those countries will actually decline in population (if you don't factor in immigration). So as countries and people get richer, they'll probably start having fewer children.
So to me, what's ideal would be for us to level off at where we are now or even drop a bit and then level off. Might be possible...
There is a widespread agreement among experts that it is in the best interest of human race to contain its population to current levels. Thus, I believe that an ideal population graph graph for human population would one representing a stable population.
It us be emphasized that that stability mus be achieved by reducing the birth rate, and not by any other means. As a matter of fact, in an ideal situation the life expectancy should rise beyond present levels and with mortality rate should decrease. Thus to maintain a constant growth rate the decline in birth rate will need to equal the expected lower mortality rate.
Moving from the ideal graph to what is practically the best possible graph for human population. I expect the population will continue to increase for about next 25 years. But the growth rate will decline as the gap between mortality rate and birth rate is reduced and finally eliminated totally by reducing birth rate.
A positive population growth rate is not sustainable in the long term by the limited resources of the earth , and a negative growth rate would imply, at least theoretically. extinction of the human race in the long run. Thus a zero population growth rate appears to be most logical. Besides, experts are reasonably sore that the current population level with some marginal increase and decrease can be sustained and maintained with acceptable levels of prosperity for a long time to come.