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World Population

Comprehension: Understanding the problem; visualizing a solution

    Questions
  1. Do you know the current world population? What units did you use in this estimate?
  2. How much do you think the population grew in the last 10 years?
  3. We will compare the population growth in the last ten years to the growth in 1950. How could your compare growth over different periods of time? Compare your ideas with others in your group.
  4. Do you think it would be useful to be able to predict future population? Why?
  5. What do you think are some important factors that influence population growth?
  6. What do you think are some of the important consequence of population growth

Acquisition: Learn or review mathematical concepts and skills needed to study population change. See the menu at the left.

Application

Information
The table below gives world population for selected years.

Year 1950 1960 1970 1980 1985 1990 1995 1999
Population (billions) 2.555 3.039 3.708 4.456 4.855 5.284 5.691 6.003

U.S. Census Report www.census.gov/ipc/www/worldpop.html

Questions

  1. What patterns do you observe from this information?
  2. Approximately how much is the world population growing each year? How did you arrive at this answer?
  3. Make points out of the data. Use a (t,P) coordinate system where t = 0 in 2000 and P is the world population, in billions. Plot the points on a (t,P) coordinate system.
  4. Use exponential regression to determine the exponential function P(t) which best fits the data. Describe in your own words exactly what P(t) describes.
  5. Graph the function P(t). Estimate from the graph the rate of change of population for 1950, for 2000 and for the current year. What units did you use to describe the rate of change?
  6. Determine the derivative P'(t). Evaluate the derivative for t = -50, t = 0 and t = current year. Compare your answers to the answer of the previous question.

Growth Rate
The growth rate is the rate of change described as a percent of the population. That is,


    7. Compute the growth rate for t = -50, t = 0 and t = current year -2000. What patterns do you notice?

The growth ratqe of an exponential function is constant.

    7. Compute the growth rate using this formula.

Reflection

Questions

  1. What assumnptions did you use in constructing the population model?
  2. Whatis the difference between the rate of population change and the growth rate?
  3. What does it mean if the growth rate is negative?


Problem
In this problem we will see what is the effect of a change in growth rate. In particular we will suppose the growth rate drops to 1% beginning in 2005.

  1. Use the function P(t) to predict the population in 2005.
  2. Write an exponential function E(t) with the following properties: the population in 2005 should be the population you predicted in a) and the growth rate should be 1%.
  3. What is a reasonable domain for this function?
  4. Compare the graphs of P(t) and E(t). Summarize what you see.