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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?
Click Here For The Solutions
For the Practice Module.