Modelling World Population Growth

Mathematical models are thrown about all over the place but they are often difficult to understand. They actually underpin a huge amount of research and development in our world and it it is great to have the chance to pursue them during the Maths Applications course. There are all kinds of things to model, but population growth is particularly topical at the moment. This is probably owing to the increasing ease with which the relevant statistics and infographics can be shared. This activity is a great, relevant example to use in class for mathematical modelling and there are lots of ways to pursue it.There is lots to follow here and more can be read about this exercise on teachmathematics.net. To start with, watch the video below and see if you can describe how the population is changing over the time period shown.

How is the world's population growing?

Watch the video below to start thinking about the answer to that question! The video shows a 'human graphic' of 200 years of population growth inspired by the Gapminder Foundation.  Each person on the grid represents approximately 93 million people. (If you are interested in recreating this graphic then follow the link above)

What to do?

Part 1 - reasoning

Having watched the video, now use the Filling the gaps activity sheet and try to fill in the gaps. You can download and print it or you can work on screen with this google sheets version. (You can make a copy for yourself or download to another format)

As you are trying to fill in the gaps, pay attention to the following points...

• What arguments are people using to justify what numbers go where?
• What language are you using to describe what you understand about growth?

When you are ready, the hidden box below shows the actual numbers that go in the gaps.... not in the right order, but they are the numbers. this can help!

Part 2 - Using technology

• Open a new file using Desmos Grapher  or another graphing package if you have a preference. (It can even be done on your GDC if you like).
• Copy the data from the google sheet in to a new table on the calculator (click the plus sign in the top left and choose table)
• Can you look at the patterns and try to read what numbers would go in between?

Part 3 - Fitting Functions

At this stage we wat to indentify the best type of function to fit the data and then find it! Based on work that you have doen with different function types, you should, for each geographical area...

• Decide what tyoe of function is most apprpriate based on both the context we are using and the data you have already
• Generate a general form of this function and neter it in to the graphing package with dynamic variables 'sliders'.
• Decide which of those variables can be fixed and which are dependent on each other.
• Adjust the others until the curve fits the data
• Use the functions to fill the gaps

Part 4 - HL - Logistic functions

Given that predictions show the propulation levelling out globally, can you fit a logistic function to the world population growth data?

Part 5 - HL - Test the model

What processes can you use to test how closely your model fits the data

Teachers Notes

The answers - The hidden box below contains the answers, as does this google sheet. You will want to use this at some point durin gthe task.

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