Exponential Growth is King

One of the big takeaways I want my students to remember about exponential functions is how powerful exponential growth is. It will outstrip linear growth ALWAYS. It grows faster than any polynomial.

To help them see this in another way, we did our first application of exponential functions today: Linear versus exponential growth in the context of population versus food supply. We used Thomas Malthus’ pamphlet from 1798 as the basis for our discussion. I found out a large amount of my students had studied Malthus last year in AP Human Geography and they remembered a LOT about him - I was impressed!

Malthus predicted that since the population of the newly founded United States would grow exponentially (doubling) and since food supply could only grow linearly, population would soon outstrip food supply, leading to starvation. He advocated for preventative checks on population to limit population growth and prevent famine.

Malthus’ predictions thankfully did not come true, a fact which amazed him. He did not take into account all the advancements humans would make in agriculture and farming techniques.

I then showed them another alarmist tone publication from the 1970’s called “The Population Bomb.” I summarized that book for them, highlighting the recommendations from the author to limit population growth (including sterilization).

Lastly, I briefly mentioned how population and food supply continue to be a focus of many scientists and other groups. Many people think access to meat will become an issue, hence the growing trend of crickets and other bugs as a source of protein. This is the Powerpoint we went through:

Right now they’re working on the packet which gives actual numbers to this scenario so they can graph them on their graphing calculators and calculate the “Point of Crisis.” We’ll look at 3 different scenarios, and by the end they should be able to summarize that not matter what we do to increase linear food supply (higher initial supply amount, higher rate of change of supply), exponential population will ALWAYS outgrow it!