World Population Growth

Here is an interesting graph. (https://ourworldindata.org/world-population-growth/) It shows the world's population growth up to the present day and then someone's estimates as to what will happen in the next few decades. It probably takes a little looking at for it to make sense. I combines two graphs in one. The horizontal axis shows the passage time in years and the vertical shows growth rates. The graph also shows the total population although these numbers are just recorded on the graph rather than being recorded on the vertical axis. As line graphs go, it's a pretty busy graph.

It seems to me that math teachers could make use of the graph in pretty much any high school mathematics class.

This actually started for me with information I found in the 2017 World Almanac. It showed population estimates going much farther back in time than this graph shows. You could look at that information as a set of ordered pairs with years being represented as x-values and world population (in billions) as y-values. The almanac states that in the year one the population was an estimated 300 million. That gave me an ordered pair of (1,0.3). Proceeding in this manner gave me ordered pairs of (1,0.3), (1250,0.4), (1500,0.5), (1804,1), (1927,2), (1960, 3), (1974,4), (1987,5), (1999,6), (2011,7).

Just using the raw data, an Algebra I class might simply write ordered pairs, or without seeing the above graph, choosing appropriately labeled axes to graph the data.

Higher math classes could look at finding an equation to model the data. I had more trouble than I thought I would. I guess that is because, as the graph shows, the rate has varied over time just in the last couple centuries, let alone millennia. Leaving out the first few ordered pairs and adjusting the data such as changing (1804,1) to (0,1) and so on, I was able to find an equation that had a correlation of r = .9647. Students could maybe experiment with similar things to get a best fitting curve.

Calculus students would be able to examine the blue population growth curve and discuss how it ties into first and second derivatives. It is interesting that the person making the future projections seems to think our current point in time seems to correspond to an inflection point. Students could discuss what that really means and mathematically and socially.