Population growth

Quantitative concepts: big numbers, exponential growth and decay

Population growth and resource depletion

by Jennifer M. Wenner, Geology Department, University of Wisconsin-Oshkosh
Jump down to: Resource Use | Exponential Growth | Prediction | Distribution | Examples & Exercises

Essential Concepts

There are 5 main concepts that our students struggle with when learning about population growth and the relationship of population to geological resource use:
  1. overpopulation is a leading environmental problem,
  2. exponential population growth and development leads to faster depletion of resources,
  3. population grows exponentially,
  4. why population prediction is difficult,
  5. population is not evenly distributed throughout the world.

A leading environmental problem: Overpopulation

Students do not understand that overpopulation is the cause of many other environmental problems. To help students understand this, one of my colleagues asks her students to list three important local and global environmental issues as part of a survey on the first day of class. During the following lecture, she presents overpopulation as the top environmental problem:
It may surprise many of you to find out that overpopulation is a leading global environmental problem. Remember on the first day of class, I asked you to list three important global environmental problems. Here are the results of those surveys:

How many of these problems are the direct or indirect result of overpopulation? Would we have such a problem with the top three -- pollution, global warming and habitat -- if world population was not so large? Other than some of the natural disasters (and even those are arguable), most of these other environmental problems are due to overpopulation.

Lifestyle affects resource use

The characterization of overpopulation as the cause of many environmental problems may be an oversimplification. Consumption of natural resources also plays an important role in straining the environment. On a global scale, it is probably pretty intuitive to students that the presence of more people in the world causes a bigger strain on natural resources. What may not be intuitive is the concept of sustainability. What does sustainability mean?
Friends of the Earth define sustainability as "the simple principle of taking from the earth only what it can provide indefinitely, thus leaving future generations no less than we have access to ourselves." Many other organizations define it in differently; however, the crux of the definition is the same. Sustainability involves living within the limits of the resources of the Earth, understanding connections among economy, society, and environment, and equitable distribution of resources and opportunities.
It is the last part of the definition that joins population growth, particularly in developed countries, and resource use. Developed countries, in general, have and use more of the Earth's resources. Population growth in developed countries puts a greater strain on global resources and the environment than growth in less developed nations. For example, in 1997, the U.S. generated 27.5% of the world's total CO2 emissions; more than five times that of India (5% of the world's total), a country with 4-5 times the population of tht U.S (Texas A&M's LABB). In fact, the way of life in the United States, on average, requires approximately 5 times the resources available on Earth today (Earthday Network).
To emphasize the disparate effects of population and lifestyle in developed vs. undeveloped countries have your students complete the "Ecological Footprint quiz" from Earthday Network. This quiz shows the participants how many "Earths" would be needed if everyone lived the way that they do. It is likely that students in the United States will find that they need approximately 5 planets to sustain their lifestyles! It may surprise them to learn this. If you want to reinforce (or contrast) the impact of undeveloped nations on resources, have your students take the quiz for an undeveloped nation. You may wish to tell them the choices to make or you may want them to make decisions about how they think people in that country live. The results may shock them.

The above makes developed nations out to be the bad guys but that is not entirely true. Undeveloped countries with large (and growing) populations also put a strain on the local environment and the limited resources that they have. Countries that struggle to meet growing demands for food, fresh water, timber, fiber and fuel can alter the fragile ecosystems in their area, putting a great strain on the limited resources that they have to draw from (ICTSD.org).

More people = More babies

Students may have a hard time understanding that population growth is controlled not only by birth and death rates but also by the present population. The mathematics of exponential growth govern the prediction of population growth. In some cases, you may want to point out that students may have heard of exponential growth in other contexts, such as compound interest or the spread of viral disease. The rate of population growth at any given time can be written:

  • r is the rate of natural increase and is usually expressed as a percentage (birth rate - death rate)
  • t a stated interval of time, and
  • N is the number of individuals in the population at a given instant.
The equation above is a differential equation and may not be appropriate for some introductory courses - - but most students in entry-level courses can handle the algebraic solution presented below.
The algebraic solution to this differential equation is

  • N0 is the starting population
  • N is the population after
  • a certain time, t , has elapsed,
  • r is the rate of natural increase expressed as a percentage (birth rate - death rate) and
  • e is the constant 2.71828... (the base of natural logarithms).
A plot of this equation looks something like the plot on the right. Population grows exponentially - if the rate of natural increase (r) doesn't change. The variable r is controlled by human behavior as described below.

Essential to understanding the mathematics of population growth is the concept of doubling time. Doubling time is the time it takes for population to double and it is related to the rate of growth. When the population doubles, N = 2N0. Thus the equation becomes

ln 2/r = t


0.69/r = t; where r is the rate and t is the doubling time.

In many ways, it is similar to half-life. But instead of the time it takes for half the isotopes to decay, it is the time it takes for a known quantity to double.

Population prediction models: Subject to change

Students (especially those in introductory classes) may have a difficult time understanding why predictions of population growth are difficult to make and constantly debated. To help them understand the difficulty of prediction have them think about the complex variables that must be considered when predicting population growth. It may be fairly obvious to students that calculation of the rate of population growth can be expressed in the following equation:
Birth rate (b)- death rate (d) = rate of natural increase (r)
Thus, population growth is directly related to:
  • current population - the number of people today has implications for future population
  • birth rate - this number is usually reported in number of births per 1,000 people per year and combined with the death rate influences the growth of population
  • death rate - this number is usually reported in number of deaths per 1,000 people per year and combined with birth rate influences the growth of population
And it may be quite intuitive to students that b - d = r. However, students may not have considered the factors that can influence both birth and death rates.
Let's think about some of the factors that may modify the birth and death rates in a region (or in the world). Do you think these things are constant throughout time? What other "variables" could change them?

There are many more variables that can affect change in the population and its growth - have your students brainstorm about other factors that affect the rate and prediction of population growth.

UNESCO and World Bank have a website with a number of learning modules on population related topics.

Wide open spaces can be hard to find

The concept of population density is sometimes difficult for students to grasp. Population density can be calculated by dividing the total population of a city (or country) by its area.

Total population / area = population density
My students mostly come from small towns and cities in Northeast Wisconsin and may not comprehend that other places in the world are far more crowded than where they live. To give them a sense of perspective, I try to give them a sense of what it is like to live in other places. For example, I tell them that in Winnebago county (the county UW-Oshkosh is situated) has a population density of 138 people/km2. On the other hand, in 1990, Kowloon (a walled part of Hong Kong) had a population density 1,924,563 people/km2 (demographia.com)! Other places of interest include: Bombay (Mumbai), India, with 39,860 people/km2 , Manhattan (New York City), United States, with 25,849 people/km2, London, England, with 4,700 people/km2 and Sydney, Australia, with about 2,500 people/km2 (wikipedia.com). Estimates of population density by city vary considerably but the general idea is that most small cities in the U.S. are not very densely populated.
I also use a story about a friend of mine who moved from China to the U.S. about 5 years ago. My friend Gong Yan moved to Atlanta from Wuhan, China, where he grew up and went to university. When he got to Atlanta, he was very uncomfortable because he felt there was so much open space. In Wuhan, when he was in a public place, he was always surrounded by people - people bumping into him, people talking to him, people streaming along the street. He would often go to a mall in Atlanta just to be around people. In contrast, many Americans become uncomfortable when in large crowds. A friend of mine traveled to Japan and tells a story of standing in line at the airport with the Japanese gentleman behind her pushing her with her body while she strained not to touch the person in front of her in line. Culturally, we deal with population density problems by changing our concept of "personal space". In many parts of the U.S., we have the luxury of significant amounts of personal space; other developing and highly urban places do not.

Examples and Exercises

Student Resources