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# EARTH MATH STUDY 0:  Practice

## United States Population

In this module, a study similar to the Introduction Module on world population is provided for you to work through. You may check your answers to Problem Set below by clicking Problem Set Answers in the menu.

### Comprehension

#### Questions

A.  Do you think that the population of the United States is increasing or decreasing?

B.  What have you noticed recently that led you to your answer to A?

C.  How do you think population change in this country might influence your life?

D.  How do you think mathematics can be used to study population change?

E.  What are some reasons for studying population change?

### Acquisition

The Table below provides resident U.S. population (in millions) for selected years.

 Year 1950 1960 1970 1980 1990 1995 US Population (millions) 152 180 204 227 249 262

Statistical Abstract of the United States

The objectives and assumptions are listed below.

#### Objectives

To determine:

1.         a linear model for United States population;

2.         the annual rate of change of United States population.

#### Assumption

The current trends for United States population continue.

### Linear Models

In this part, you will find a linear function to approximate data for United States population and use this to

     estimate annual population growth,

     estimate the population for years other than those in the data set, and

     forecast future population size.

(Round off to three places for this work.)

#### Problem Set

1.         Plot the points corresponding to the data in Table 1.  The first coordinate is year; denote this by t with t = 0 in year 2000.  The second coordinate is population in billions.

2.            Determine the linear regression function that best fits these data; call this function S(t).  Graph the function S(t) on the same coordinate system as the plot of the data points.

3.         What is the slope of S(t)?  Give a verbal interpretation of the answer; identify units clearly.

Use the function S(t) to answer the following questions.

4.         What is the annual population growth?

5.         How much will the population grow in 10 years? Six months? One week?

6.            Estimate the population in the year 2005.

7.            Predict when the population will reach 300,000,000.

### Reflection

#### Questions

A.        Do you think that a linear function is good to use for this study?  Are there other functions that you think might provide a better model?  Why?

B.        How long do you think this model will be accurate; i.e., what is a reasonable domain for the function?

C.        How do you think the predicted increase in United States population might affect future life in the U.S.?  In the World?  In your home town?  