Exponential Growth and the Rule of 70
Six billion living, eating, breathing, refuse-making people live on the planet we call home. Is that a large number of people or is it relatively small? How do that many humans impact the earth? Will we run out of room? Will we run out of food? Will we all have clean water to drink and clean air to breathe? In some parts of the world, we are already running out of room; people are stacked on top of each other like so many chickens in cages. In places such as Mexico City, the poor live in areas so crowded that streams of raw sewage flow through them and the air they breathe is filled with dried fecal matter blowing in the wind. Is "six billion people" a lot? You bet it is. And it's only getting worse. But how do we make projections in regards to how many people there will be in the future? To answer this question, let's look at the mathematics of population growth.
A quantity grows exponentially when it increases by an amount that is proportional to how much of the quantity is already there. Fore example, a colony of yeast cells in which each cell divides into two new cells every 10 minutes is growing exponentially. For each single cell, after 10 minutes there will be two new cells. After another 10 minutes there will be four cells, 10 minutes later there will be eight cells, and then sixteen, and then thirty-two and so on. The more yeast cells there are, the more new ones can be made. On the other hand, a quantity grows linearly when it increases by a constant amount in a constant period of time. If a construction crew builds one mile of road per week, the length of the road increases linearly. The increase does not depend on how much road is already there.
Populations grow exponentially, though over time the rate of growth tends to naturally slow down. It would be impossible for populations to double forever because we'd simply run out of matter on the earth if they did. As the growth rate slows, the population levels off to what we call the carrying capacity and we define the carrying capacity to be the maximum population that an environment can sustain indefinitely.
How powerful is exponential growth? Try this exercise. Take an 8-1/2" x 11" piece of printer paper (about 0.0035 inches thick) and begin folding it in halves. After folding it in half once, the thickness has doubled. Folding it in half once more again doubles the thickness. You can probably fold it in half at most about six more times, unless you possess superhuman powers. If you could continue to fold it in half say 42 times, how thick do you think the paper would be? A few inches? More than a foot but less than a mile? The truth is, the paper would stretch from here to the moon! And that is the power of exponential growth: doubling and redoubling. This surprises most people because most people think linearly and they assume this type of growth to be a linear process, which it definitely is not.
We'll close by saying that "population" is an extremely complex issue. Lots of different factors go into predicting future growth and carrying capacity. Have we already overshot the Earth's carrying capacity? Or do we still have room to grow? Are there enough resources to go around for everyone or just for those with political and financial clout? So many questions, so few answers.
- Every three years, the world's population increases by about the current population of the United States. How many people per second is this? Does this sound like a large number?
- How fast is your hometown growing? What is its doubling time?
- Does your hometown have room to grow? Or has it reached its carrying capacity?
- As your hometown grows, what kinds of stress are put on its infrastructure?
- Exponential Growthhttp://www.intsoft.com/powers2.html
Raju Varghese gives an excellent presentation on the power of exponential growth. He gives several examples that make the concept of doubling very understandable.
- Exponential Growth Tutorialhttp://www.krellinst.org/UCES/Demo/ScientificComputing/uces-4/uces-4/uces-4.html
Joseph Zachary developed this tutorial on exponential growth for the Hamlet Project at the University of Utah.
- Exponential Growth and the Rule of 70http://www.ecofuture.org/pop/facts/exponential70.html
Fred Elbel wrote this excellent essay on exponential growth and the doublings of populations. He includes examples and links to other references.
- Population Expohttp://www.popexpo.net/english.html
This web site explains many aspects of population growth in terms that the average person is able to relate to. This site has plenty of interesting facts about world population and problems that are associated with it.
- Population Action Internationalhttp://www.populationaction.org/
This site has lots of information, including resources and multimedia links. The site is updated on a daily basis.
- Population Reference Bureauhttp://www.prb.org/
This is an excellent multi-language site with world population data. The data is also downloadable in Adobe(r) Acrobat format and includes current population, growth rates, fertility rates, infant mortality rates and more.
- The Population Councilhttp://www.popcouncil.org/
According to the website, the Population Council's mission is to improve the well-being and reproductive health of current and future generations and to help achieve a humane, equitable, and sustainable balance between people and resources.
- The United Nations Population Fundhttp://www.unfpa.org/
The official website of the UNFPA, devoted to improving the quality of reproductive health care and family planning for those countries that request assistance.
All material (except for some code and external links) © Jeffery A. Schneider, 2003