Quantitative concepts: big numbers, exponential growth and decay
Population growth and resource depletionby Jennifer M. Wenner, Geology Department, University of Wisconsin-Oshkosh
Jump down to: Resource Use | Exponential Growth | Prediction | Distribution | Examples & Exercises
Essential ConceptsThere are 5 main concepts that our students struggle with when learning about population growth and the relationship of population to geological resource use:
- overpopulation is a leading environmental problem,
- exponential population growth and development leads to faster depletion of resources,
- population grows exponentially,
- why population prediction is difficult,
- population is not evenly distributed throughout the world.
A leading environmental problem: OverpopulationStudents 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:
- Pollution (unspecified):14.7%
- Global warming:14.5%
- Air pollution:13.5%
- Habitat destruction:13.1%
- Resource depletion/degradation:11.8%
- Population growth/Overpopulation:7.9%
- Natural disasters:6.2%
- Water pollution:6.6%
- fossil fuels (oil spills/ANWR):6.0%
- Waste management:3.5%
- Miscellaneous (famine, poverty, ignorance, etc):2.3% compiled from Dr. Maureen Muldoon's Environmental Geology course, Spring 2005, UW-Oshkosh
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 useThe 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?
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 babiesStudents 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.
- 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).
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
or0.69/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 changeStudents (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:
- 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
- age structure of the population - the number of women of child bearing age affects the rate of population growth.
- total fertility rate - Total fertility rate (TFR) is the average number of children that each woman will have in her lifetime and affects the birth rate.
- health care - the quality and availability of health care in an area can affect both death rate (by increasing average life expectancy) and birth rate (babies are more likely to survive past childhood). Access to immunizations, family planning and birth control are also important to the overall picture of population growth.
- education - Birth rates tend to fall in countries where the population has access to education
- jobs - Birth rates also fall off when unemployment is low.
- standard of living - Birth rates are lower where standards of living and quality of life are high. Unfortunately, standards of living are difficult to raise in areas where population growth is high - this creates a negative feedback loop that is difficult for some countries to get out of.
- immigration/emigration - the number of people entering or leaving a country (area) actually changes the N0 and changes population in a more complex way than by altering birth rate or death rate.
- development and industrialization - these two factors alter population growth in complex ways. They can affect an area's income and, thus, its access to many of the factors listed above. Higher income/more developed countries have lower birth and death rates
- disease - in a given year (or even decade) epidemics of infectious diseases can increase death rate dramatically, particularly for a specific area. For example, the bubonic plague decimated Europe in the 14th century - the population of Europe was cut nearly in half by 1400.
- war/political upheval - War and political upheval can also increase death rates.
- climate - Natural disasters such as drought or flooding can affect food resources and the population will be affected accordingly.
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
Examples and Exercises
Two World Population activitiesThe 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.
- 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 ( This site may be offline. ) .
- The Population Reference Bureau (more info) has all sorts of great information on almost every country; birth rates, death rates, GDP, health, environment, etc.