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EARTH
STUDIES
Introductory
Module
World
Population
Introduction
In this module,
you will be introduced to the format and methods that will be
used in the analysis of data and solution of problems that are
presented in Earth Studies. The Studies will all be presented
in a somewhat structured format that will be outlined in this
module. Applets, or little programs, have been designed
to be used with each Study; these will perform the mathematical
operations you need to analyze data and build mathematical modules.
Also, links are included throughout each study that will take
you to explanations of mathematical terms and methods. Here
you will be guided through a study on population that will illustrate
the most common methods used in all of the Earth Math Studies
and will also illustrate the use of the applets. First,
we outline the general structure for all the Studies.
Each
Study will have three components:
 the text,
which will provide information about a particular issue and
ask questions;
 the Menu
will be in two parts: the Tool Chest, which will contain the
applets to perform the mathematical operations; and a Topics
list, which will contain links to explanations of relevant mathematical
topics;
 the journal,
which will be the place where you can record your thoughts,
answers, and mathematical solutions.
The text will
be presented in four sections: Comprehension; Acquisition;
Application; and Reflection.
 The Comprehension
section will provide information about the issue and ask pertinent
questions for you to think about and express your own ideas
regarding the issue.
 The Acquisition
section will provide more detailed information, relevant data,
or direct you to a website to acquire more information or data.
 The Application
section will ask specific questions which will require mathematical
analysis that will lead to a mathematical model. The model
should be able to provide answers to questions raised regarding
the issue. It is in this section that the applets will
be used.
 The Reflection
section will ask questions regarding the reasonableness or validity
of your model.
The Tool Chest
will be the place where you can access the applets that will perform
the mathematics. Here you can enter your data or other quantitative
information and use the applets to analyze data and construct
mathematical models. The results should answer the questions
involved in the issue.
The journal
will be the place you record your answers to questions from the
text and include the explanations of the mathematics you used.
Your journal should be written as a file in the word processing
package on your computer; this will be the document you turn in
to your instructor.
EARTH
STUDY: WORLD POPULATION
Comprehension
In
this section, questions are posed that are designed to stimulate
your thoughts and observations regarding population increase/decrease,
reasons for studying population change, and methods that might
be used. At this point, you should open a blank document in your word processor
and record your answers to these questions.
Copy each question into the journal and type your response
below in a different color or font. Be sure to write
in complete sentences and express your ideas so that others can
understand. Save your work and keep this window open throughout
this study so you can easily record other questions and answers.
Questions
A. Do
you think that the population of the World 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 the world 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
In
this section, you will be given information about population increase,
data is provided, and links to websites that contain more information
and updated data.
Estimates
of world population before the twentieth century vary widely,
but most sources put the number of people in the world in 1750
at about 750 million. By midnineteenth century the population
reached 1 billion and until 1930 the growth was never more than
1%; however, since 1950 the increase has never fallen below 1.6%.
Current patterns of population growth and the accompanying changes
in consumption are placing increasing stresses on ecosystems through
environmental degradation, deforestation, loss of biological diversity,
over harvesting, and accumulation of toxic wastes.
The Table
below gives the United Nations estimates of the world population
(in billions) every five years from 1950 1995.
World Population

Year

1950

1955

1960

1965

1970

1975

1980

1985

1990

1995

Population
(billions)

2.554

2.779

3.038

3.345

3.704

4.086

4.457

4.856

5.295

5.732

World Watch
1996
In this
section, objectives and assumptions are stated;
these will determine your mathematical model for population. You will use relevant mathematical tools that are
provided on the applets to perform the analysis on the data
and build your models. You will develop a model for world
measure population growth. Applets can be accessed by
clicking “Tool Chest” on the Menu to the left of the screen.
You should
follow the steps outlined after each question to familiarize
yourself with the techniques used and the applets available.
Record answers in your journal.
The objectives
and assumptions are listed below.
Objectives
To determine:
1. a
linear model for world population;
2. the
annual rate of change of world population.
Assumption
The current
trends for world population continue.
Application
Linear
Models
In this
part, you will find a linear
function to approximate data for world 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
The applets
needed needed to complete this problem are provided in the text
for this Introduction module. Usually, you will need to follow
these steps.
 Scroll
down to “Tool Chest” on the menu to the left of the screen.
 Click
“linear regression” (since we are looking for a linear function).
The linear
regression applet will open in a separate screen.