The Navajo Reservation is the largest Indian reservation. About 25,000 square miles of reservation land extend across northeastern Arizona and adjacent New Mexico and Utah. The reservation, an area that is larger than several states, is about the same size as West Virginia. The human population density of the reservation is about six people per square mile, a greater density than Nevada, but far below the average of about sixty people per square mile for the entire United States.
Economic development has the potential of producing radical changes when coupled with the social pressures brought about by population growth. For the Navajos, the real danger of too many people for the land resource base continues to hang like a specter over the horizon.
In this study, we will look at the population of the Navajo community.
1. Do you think that population on the Navajo reservation is increasing or decreasing?
2. How do you think population change might influence your life?
3. Do you think population in the United States is increasing or decreasing? Why?
4. How can we use mathematics to study population change?
5. What radical changes are brought about by population growth?
Mathematical Topics
Learn or review mathematical concepts and skills needed to study population predictions. See menu at the left.
Information
The Table below provides the Navajo population in the indicated year.
|
YEAR (x) |
POPULATION P(x) |
|
1855 |
7,500 |
|
1869 |
7,151 |
|
1875 |
11,768 |
|
1885 |
21,003 |
|
1895 |
20,500 |
|
1905 |
26,390 |
|
1922 |
30,052 |
|
1931 |
41,281 |
|
1947 |
56,000 |
|
1958 |
85,000 |
|
1970 |
105,000 |
|
1975 |
151,354 |
|
1980 |
160,000 |
|
1981 |
166,519 |
Source: Bureau of Indian Affairs and U.S. Census Office.
Apply mathematical knowledge and calculator operations to analyze population changes in the Navajo Nation. The equation will be based on data recorded over past years and can be used to predict future population changes.
1. We define our variables: x = years after 1850, i.e., x = 0 in 1850, and P = Navajo population. Make points from the data provided; the first coordinate will be x (year) and the second will be P, Navajo population.
2. Using regression, fit a quadratic equation to the data. Write the linear equations in the standard form P = ax2 + bx + c. Round coefficients to one decimal place.
3. In what year will the Navajo population reach 150,000?
4. Use the regression line to predict the population this year. in the year 2010?
5. What is the population increase this year? in the year 2010? in the year 2030?
6. Predict the number of people per square mile in 2050.
Examine solutions and implications.
1. Do you think population predictions are necessary?
2. How do we know what kind of model to use?
3. How accurate is your prediction? How far in the future do you think you can predict?
4. When and by what means will it be necessary to re-evaluate your model and predictions?