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World Population PreCalculus Version

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.

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 http://www.census.gov

Application

Questions

1. How much did the population change between 1950 and 1960? What was the average annual change for that period? State the units clearly.
2. Repeat question 1 for the period between 1970 and 1980; between 1990 and 1995.
3. Do you think a linear model would be good for these data? Explain your reasoning. How about an exponential model?
4. Create an exponential model. For this question, use exponential regression.
5. a) Plot the data on from the (t, P) coordinate system where t = 0 in 2000 and P is the world population at time t (in billions).
b) Use exponential regression to derive the function which describes the world population (in billions) at time t.  Graph the function and call it P(t).

6. Use the function P(t) to answer these questions.
7. a) What was the world population in 1946?
b) When did the population reach 5 billion?
c) How many years did it take for the population to increase from 2 billion to 3 billion?
d) How many years did it take for the population to increase from 3 billion to 4 billion?
e) How many years will it take for the population to double its current level?

8. Determine the change in population from the beginning to the end of the given years.
9. a) 1950
b) 2000
c) 2005

10. The rate of change of the population over a period of time is the change in population divided by the change in time. Determine the rate of change of the population for the given periods of time. State your units clearly.

a) January 1,2002 to January 1, 2003
b) January 1, 2002 to July 1, 2002
c) January 1, 2002 to April 1, 2002
d) January 1, 2002 to January 2, 2002

## Reflection

1. Reflect on the computation

a. What did you do to predict the population at a particular time?
b. What did you do to predict when the population will reach a particular level?

2. Reflect on the graph

a. Do you think the rate of change of population is the same now as it was 50 years ago?
b. If you had used a linear model, what differences would that have made in your predictions?

3. Reflect on the interpretations

a. How can you compare population change over different intervals of time?
b. What occurrences might lead to slower population growth?