Why certain countries have linear growth versus exponential growth

The World’s Population Hasn’t Grown Exponentially for at Least Half a Century

Explanation:

Recently I was looking at some data about world food production on the excellent Our World in Data site, and I discovered something very simple, but very surprising about the world’s population. We often hear (and I used to teach) about the threat of an exponentially growing population and the pressure it is supposed to be putting on our food supply and the natural resources that sustain it (land, water, nutrients, etc). But I found that the global population isn’t growing exponentially, and hasn’t been for at least half a century.

It has actually been growing in a simpler way than exponentially—in a straight line.

What exponential growth is

Exponential growth (sometimes also called geometric or compound-interest growth) can be described by an equation in which time is raised to a power, i.e. has an exponent—hence the name. But it also can be described in simpler terms: the growth rate of the population, as a fraction of the population’s size, is a constant. Thus, if a population has a growth rate of 2%, and it remains 2% as the population gets bigger, it’s growing exponentially. And there’s nothing magic about the 2; it’s growing exponentially whether that growth rate is 2% or 10% or 0.5% or 0.01%.

Another way to put it is that the doubling time of the population—the number of years it takes to grow to twice its initial size—is also a constant. So, if the population will double in the next 36 years, and double again in the following 36 years, and so on, then it’s growing exponentially. There’s even a simple rule-of-thumb relationship between doubling time and the percentage growth rate: Doubling Time = 72/(Percentage Growth Rate). So that population with a 36 year doubling time, is growing at a rate of 2% per year.

But probably the simplest way to describe exponential growth is with a graph, so here’s how it looks:



Figure 1. Exponential growth versus linear (straight-line) growth.

This graphic not only shows the classic upward-curving shape of the exponential growth curve, but also how it contrasts with growth that is linear, i.e. in a straight line. Additionally, it demonstrates a simple mathematical result: if one quantity is growing exponentially and a second quantity is growing linearly, the first quantity will eventually become larger than the second, no matter what their specific starting points or rates of growth.

This isn’t just abstract math; it also illustrates the most famous use of exponential growth in political debate. It was put forward by the English parson Robert Malthus over two centuries ago. He argued that the human population grows exponentially while food production can only grow linearly. Thus, it follows inevitably that the population will eventually outgrow the food supply, resulting in mass starvation. This is the case even if the food supply is initially abundant and growing rapidly (but linearly). The upward-bending-curve of an exponentially-growing population will always overtake it sooner or later, resulting in catastrophe.