Modelling World Population Growth

So you will have seen Simon Gregg's post about our joint project (Secondary, primary, maths and Geography) 'If the World was a village' The great thing about this exercise was the way that so many students of different subjects and different ages could be involved! This blog post is about how year 12 IB Maths Studies students had a go a modelling population growth. (A good summary of the whole project with lots of photos and videos can be found here.)

To stat with - watch this video and see if you can describe how you think the population growth is growing. Each person represents 93 Million and the worlds population has been organised in to 4 geographical regions - Asia, Europe, The Americas and Africa...

What do you think? We asked students to fill in the blanks on this table....

 This exercise prompted lots of fabulous reasoning about how the population was growing in different regions. For example what do you put in between 0.10 and 0.21? Should it go half way? What kind of growth would that be? We had a lot of discussion around this exercise and concluded that we wanted to try and fit an exponential model to the data! Here are some of the results....

Here we discovered that we could use an exponential model up until the present day for world population growth, but that predictions for there after suggested that that our model would give an inaccurate prediction.

For Africa on the other hand..... it looks like population will continue to grow exponentially!

The Americas seem to follow the pattern of the whole world....

As does Asia...

We tried hard but could not really fit an exponential model to population growth in Europe.

This is where it becomes really interesting to look at what happens when we look at how the population of the world is changing by proportion. The next video shows the world as a village of 100 people, changing from 1810 onwards. This is a tricky idea, because there are always 100 people in the picture even thought the number of people they represent changes. Look what happens to the number of Europeans!

The whole activity prompted lots of discussion and reasoning and was a fine demonstration of exactly why mathematics is such an important tool for understanding our world.