Quantitative concepts: big numbers, exponential growth and decay

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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:

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? 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).

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:

Where:

• 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.

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

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: 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.

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.

Examples and Exercises

• Teaching functions in an introductory course

  This exercise includes a template for teaching functions in introductory courses and a complete exercise (ready to use) for teaching about population growth. There are also links to interesting pages with population data.

• World Bank learning module on Population Growth Rate

  This website is part of the World Bank Group's educational site with modules that address sustainable development in the world. There are a number of activities that can be used by educators to help students understand population growth rate.

• Earthday's Ecological Footprint quiz

  This is the opening webpage for the "Footprint" quiz on Earthday's website. It takes one through a number of questions about standard of living and lifestyle and estimates how "sustainable" one's way of life really is.

• Two World Population activities

  The SERC Starting Point site has two activities, students explore models of population with Excel and students compare models to actual data. Each has an activity sheet (as PDF) that can be downloaded and handed out to your students.

Student Resources

• The UN Population division has a website about World Population Prospects that has downloadable data regarding many important population variables.
• Mark Francek at Central Michigan University provides links to several other sites with population data (more info) .
• The Population Reference Bureau (more info) has all sorts of great information on almost every country; birth rates, death rates, GDP, health, environment, etc.