The answer: not any more.

A discussion with Joss Winn raised my interest in the question of whether human population growth is really exponential in any strict sense.  Joss referred to Fred Pearce's post The Overpopulation Myth, about how world population growth is slowing.  I decided to study the figures.

Here's a graph of world population over the past 2000 years.  Data and the UN sources are listed at the end of this post.  The data points are marked: they are more frequent the closer we get to the present day.

This looks familiar: it appears to be what we think of as an exponential curve, growing more and more rapidly over time.  But does it really follow an exponential pattern in detail?

Steady exponential growth occurs when a quantity increases at a fixed multiplicative rate over equal intervals of time, for example, if it grows by a fixed percentage, p% say, of its value every year.

So let's graph the annual percentage growth rate between each pair of data points:

Steady exponential growth would be occurring if the above curve were a horizontal straight line, at an equal height all the way across the graph, showing an unchanging growth rate of p% for some value of p.

For example, on the face of the data, this seems to be roughly true between around 1000 and 1400: during that period, fairly steady exponential growth apparently did occur, at a (quite low) rate of around 0.09% to 0.1% per year (see the data table).  Of course, there are very few data points to go on at that time, and the Black Death (about 1350) must have interfered with population growth.  But anyhow, around 1500 or so, the growth rate started to go up.

Let's look at more detail, in a subsection of the same growth rate graph, but focusing on the period from 1775 to the present:

Again we see a period of apparent fairly steady exponential growth: between say 1780 and 1900, the growth rate was between 0.43% and 0.54% per annum: about 0.5% a year.

Then (perhaps from the end of the First World War) growth speeded up rapidly, impeded only for a time by the Great Depression and the Second World War, reaching an all-time peak of a little over 2% per year some time around 1968, give or take a couple of years.  Since then, the growth rate has declined.

Fred Pearce discusses the reasons for this decline in his post, listing the principal cause as better sanitation and healthcare allowing more babies to grow up, meaning that fewer births are needed to "ensure the next generation".

We seem to be able to conclude that human population growth over the past 2000 years has only been steadily exponential for certain not prolonged periods.  It has sometimes been faster than (a fixed-rate) exponential; but—fortunately for the planet—we are past that point and the growth rate is now decreasing. Some future maximum population can be envisaged.  The 1999 UN World at Six Billion report (link below) suggested stabilisation at "just above 10 billion" after 2200; however, the fluctuations for the twentieth century in the growth rate graph above, not to mention the tribulations we now face, give a sense of uncertainty about what is to come.

Pearce notes that this good news about population is not nearly enough.  Economic growth (with the environmental destruction it brings) is overwhelmingly through increase not in human numbers but in consumption per head.

Data

The population figures before 1950 are from Table 1 in the UN's 1999 World at Six Billion report.  From 1950 on, the population figures, with more accuracy, are from an online UN data source, the World Urbanization Prospects 2009 Revision Population Database.  The percentage annual growth figures over the intervals between the consecutive population figures are calculated and attributed at the midpoint of each interval.

It's worth noting that if the maximum growth rate, 2.04% round 1968, had continued steadily, world population would have doubled in about 34 years.  Continuing at the 1.2% 2007 growth rate would lead to doubling in about 58 years, much longer, showing how seemingly small changes in growth rate do have a big effect.