Teacher Background Information:
No discussion of the future of our planet can go
Content Area:
Linear Algebra,
Linear and Exponential without a consideration of the impact of population.
Students will need to look at this issue as a framework for all other data regarding environmental, economic and social equity.
Goals: To apply statistical modeling tools to world population data. The models that students develop will then be used to predict the population of the world in 2050.
Objectives: Students will . . .
 Calculate ratios and percentages.
 Represent data via circle graphs.
Functions
Linear and Exponential
Regression Models,
Percent operations,
Rounding
Prerequisites: Linear
Algebra; Writing Equations
Of a line
Standards met:
NM-Num.9-12.1a
NM-Num.9-12.2a
NM-Num.9-12.3
NM-Alg.9-12.1a,e,f
NM-Alg.9-12.2c
 Use exponential equations to make calculations.
 Will use multiple math tools to analyze data.
Model data using trend lines and the regression
 capabilities of the graphing calculator
Procedure:
 Ask students to read the article “Population and the Environment: The Global Challenge”.
 Lead a brief discussion as to each of these points and how some of the pressures on the earth might be alleviated if the population was
NM-Alg.9-12.3
NM-Alg.9-12.4
NM-Data.9-12.1
NM-Prob.Pk-12.1,2,3,4
NM-Prob.Comm.Pk-12.1,2,3,4
NM-Prob.Conn.Pk-12.1,2,3
NM-Prob.Rep.Pk-12.1,3
Time required: 1-2 class periods
Materials: cut in half, a third, etc.
 Hand out the Global Population by Continent
Analyze Data Using Pie Charts student sheet.
 Review and answer any questions.
Graphing Calculators
Protractors
 Give students time to complete the sheet.
 Hand out the World Population: An Explosion or a Hic-up? Student Sheet
 Review and answer questions.
 Give students time to complete the worksheet.
 Have students read the article, “How many people can the earth support?
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Name: ____________________________ Class Period:______________
When studying population growth and sustainability it is important to be acquainted with how the world’s population is distributed today. In this problem you will;
First: Make a pie chart to illustrate world population distribution in the year 2008.
Second: Use historical growth data to predict the world population for the year 2050.
Third: Make a new pie chart illustrating the projected world population distribution in the year 2050.
Fourth: Compare and contrast the 2005 World Population pie chart with the 2050 World Population pie chart
1. Using continental population data from the U.S. Census International Data
Base. A. Calculate the world population total.
B. Calculate the percent of total for each continent.
C. Calculate the size of the pie slice for each continent.
Continent
Africa
Population 2008
972,752,366
Percent of Total Slice (sector) size
Asia
Europe
Oceania
North America
South America
4,053,868,153
729,553,228
34,368,042
527,831,687
388,619,456
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2. Create your pie charts on the first circle on the following page. Use a protractor to approximate each slice. ‘Fudging’ a little is OK. Be sure to give your graph a title and label each sector.
3. The annual population growth rates (in percent) for each continent during the years 2000 to 2005 were: Africa: 2.2%, Asia: 1.2%, Europe: 0%, Oceania:
1.3%, North America: 1.0%, and South America 1.4%. (Statistical Yearbook
2007; Statistics Norway)
Use the exponential growth formula to find the expected continental population for the year 2050. Record your results in the chart below.
2050 Population = (2008 population)(1 + r) t r = rate of population growth (2.2% = .022) t = the number of years from 2008 until 2050
Example: AFRICA 2050 Population = (972,752,366)(1.022) 42
= 2,426,274,419 people
Continent
Africa
Growth rate (r)
Projected
Population 2050
(millions)
2.2% 2,426,274,419
Percent of
Total
Slice (sector) size
Asia
Europe
Oceania
North America
South America
TOTALS
After calculating total world population, find the values for columns 4 and 5.
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4. Create a second pie chart in the space below. Be sure to give the graphs a title and label each sector.
5.
Which continent experienced the greatest increase in population growth?
6. Which continent experienced the greatest percent increase in population?
7. Given a continuation of current growth rates, will Africa’s population ever exceed Asia’s population? Explain?
8. Given a continuation of current growth rates, will North America’s population ever exceed Africa’s population? Explain?
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9. Use the table on your graphing calculator to determine how long it will take for North America’s population to exceed the population of Europe.
__________________________________________________________________
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Teacher Key
Name: ____________________________ Class Period:______________
When studying population growth and sustainability it is important to be acquainted with how the world’s population is distributed today. In this problem you will;
First: Make a pie chart to illustrate world population distribution in the year 2008.
Second: Use historical growth data to predict the world population for the year 2050.
Third: Make a new pie chart illustrating the projected world population distribution in the year 2050.
Fourth: Compare and contrast the 2005 World Population pie chart with the 2050 World Population pie chart
1. Using continental population data from the U.S. Census International Data
Base.
A. Calculate the world population total. 6,706,992,932
B. Calculate the percent of total for each continent. Continental Population
6,706,992,932
C.
Calculate the size of the pie slice for each continent. Answer in B *360
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Continent Population 2008 Percent of Total Slice (sector) size
Africa
Asia
972,752,366
4,053,868,153
0.145 = 14.5%
0.604 = 60.4%
52º
218º
Europe
Oceania
North America
South America
729,553,228
34,368,042
527,831,687
388,619,456
0.109 = 10.9% 39º
0.005 = 0.5%
0.079 = 7.9%
0.058 = 5.8%
2º
28º
21º
2.
Create your pie charts on the first circle on the following page. Use a protractor to approximate each slice. ‘Fudging’ a little is OK. Be sure to give your graph a title and label each sector.
3. The annual population growth rates (in percent) for each continent during the years 2000 to 2005 were: Africa: 2.2%, Asia: 1.2%, Europe: 0%, Oceania:
1.3%, North America: 1.0%, and South America 1.4%. (Statistical Yearbook
2007; Statistics Norway)
Use the exponential growth formula to find the expected continental population for the year 2050. Record your results in the chart below.
2050 Population = (2008 population)(1 + r) t r = rate of population growth (2.2% = .022) t = the number of years from 2008 until 2050
Example: AFRICA 2050 Population = (972,752,366)(1.022) 42
= 2,426,274,419 people
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Continent Growth rate (r)
Projected
Population 2050
(millions)
2.2% 2,426,274,419
Percent of
Total
Slice (sector) size
Africa
Asia 1.2% 6,690,385,536
Europe
Oceania
0%
1.3%
729,553,228
59,122,323
North America 1.0% 801,665,432
0.213
=21.3%
0.587
=58.7%
77º
211º
0.064 =6.4% 23º
0.005 =0.5% 2º
0.070 =7.0% 25º
South America 1.4% 696,816,858
TOTALS 11,403,817,798
0.061 =6.1% 22º
100% 360º
After calculating total world population, find the values for columns 4 and 5.
4. Create a second pie chart in the space below. Be sure to give the graphs a title and label each sector.
World Population by Continent
2008
1
2
3
4
5
Africa
Asia
Europe
Oceanla
Nort h
America
South
America
6
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2050
1
2
Africa
Asia
3
Europe
4
Oceania
5 North America
6
South
5. Which continent experienced the greatest increase in population growth?
Asia has the greatest increase. Its population increased by 2,636,000,000
6. Which continent experienced the greatest percent increase in population?
Africa experienced the greatest percent increase of almost 60%
7. Given a continuation of current growth rates, will Africa’s population ever exceed Asia’s population? Explain?
Yes, because Africa has an exponential growth rate that is greater than Africa’s. Africa’s population will exceed China’s in 146 years at current growth rates.(approximately)
8. Given a continuation of current growth rates, will North America’s population ever exceed Africa’s population? Explain?
No, North America’s population is growing at a slower exponential rate than
Africa’s population. The population of North America will always be less.
9. Use the table on your graphing calculator to determine how long it will take for
North America’s population to exceed the population of Europe.
In approximately 33 years North America’s population will exceed Europe’s
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Name: ____________________________ Class Period:______________
Goal: In this problem you will graph world population over time. Then you will explore which function; linear, quadratic or exponential, best models this data.
1. Round world population to the nearest hundred million.
Year Total World Population Total World Population
(rounded)
2.6 billion
1955 n= 5 2,780,907,497
1965 n = 3,349,157,095
1975 n = 4,089,026,773
1985 n = 4,852,574,467
1995 n =
2000 n =
5,690,982,026
6,084,907,596
2. Graph World Population data below. Be sure to give the graph a title and label each axis.
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3. Draw a trend line (also know as a line of best fit) that goes through the middle of the data set. Your best line will meet two characteristics a. The total vertical distance to the trend line from the data points above the trend line will (as close as possible) equal the total vertical distance from the data points below the trend line to the trend line. b. The total vertical distance for all points is as low as possible.
4. Select two points on your trend line.
1 st point: _________ 2 nd point: ________
Write the equation of the line that goes through these two points.
Equation: ________________________________
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5. a. What does the slope represent? b. What does the y-intercept represent? Be specific.
6. Enter this data into your graphing calculator. Find the linear regression equation (LinReg) and its corresponding correlation coefficient. (Hint: touch
Catalog: go to turn diagnostic on enter)
Linear: _________________________________________ r = _______
7. Compare the equation of your trend line to the linear regression. Are the two close?
Describe what you could do to make your trend line more like the LinReg line?
8. Now you will examine two other regression models, quadratic and exponential.
Quadratic: _______________________________________ r = _______
Exponential: ______________________________________ r = _______
Answer the following questions:
1. Which curve fits the data best; linear, quadratic or exponential? Explain.
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2. Sketch the curve with the highest R 2 value onto the graph above. (Note: do not round off)
Predict World Population for the year 2005
3. Enter the regression equations into your graphing calculator. (Note: do not round off.) Go to the table scroll down to n= 55 = 2005. Record the predicted population for 2005.
Method
Predicted World
Population for 2005
Linear
Regression
Quadratic
Regression
Exponential
Regression
4. The actual population for 2005 was 6,470,340,436. Compare this total with the predicted values from the above table. Which equation was closest?. Any surprises??
Predict World Population for the year 2050
5. This time go to the table scroll down to n = 100 = 2050 and record the predicted population for 2050.
Method
Predicted World
Linear
Regression
Quadratic
Regression
Exponential
Regression
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Population for 2050
6. How old will you be in the year 2050? ______________
7. Which population prediction do you think is most accurate?
8. How much will the world population have increased since 2005?
Population Change: __________________
Percent increase in Population: ___________________
9. Do you feel that the planet can sustain the predicted world population in
2050? Please share your thoughts. Please write in complete sentences .
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Teacher Key
Name: _________________________ Class Period:______________
Goal: In this problem you will graph world population over time. Then you will explore which function; linear, quadratic or exponential, best models this data.
1. Round world population to the nearest hundred million.
Year Total World Population Total World Population
(rounded)
2.6 billion
1955 n= 5 2,780,907,497
1965 n = 3,349,157,095
1975 n = 4,089,026,773
1985 n = 4,852,574,467
1995 n =
2000 n =
5,690,982,026
6,084,907,596
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2. Graph World Population data below. Be sure to give the graph a title and label each axis
.
Time in Years
3. Draw a trend line (also know as a line of best fit) that goes through the middle of the data set. Your best line will meet two characteristics
1. The total vertical distance to the trend line from the data points above the trend line will (as close as possible) equal the total vertical distance from the data points below the trend line to the trend line.
2.
The total vertical distance for all points is as low as possible.
4. Select two points on your trend line. 1 st point: __ (0,2.45) _ 2 nd point:
__ (15,3.5) _ Write the equation of the line that goes through these two points.
Equation: ___ P(t) = 0.07t + 2.45
__ * Answers will vary ____________
5. a. What does the slope represent? b. What does the y-intercept represent?
Be specific.
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a. The slope 0.07 represents a 0.07 billion increase in the world population per year. b. 2.45 represents world population in 1950, the starting point of this statistical study.
6. Enter this data into your graphing calculator. Find the linear regression equation (LinReg) and its corresponding Pearson correlation coefficients. (Hint: touch Catalog: go to turn diagnostic on enter)
Linear: _ P(t) = 0.0727t + 2.3636
________________________ r = ___ 0.9955
___
7. Compare the equation of your trend line to the linear regression. Are the two close?
Yes, my rate estimate was a growth of 70 million/yr. LinReg estimates a growth rate of 72million/year.
Describe what you could do to make your trend line more like the LinReg line?
Really, not much. But I might drop the left side somewhat while raising the top.
8. Now you will examine two other regression models, quadratic and exponential.
Quadratic: __ P(t) = 0.000429x 2 + 0.05128x + 2.5244
_____ r 2 = _ 0.9978
_
Exponential: _ P(t) = 2.575 • (1.01797) t ____________ r 2 = _ 0.9980
_
Answer the following questions:
1. Which curve fits the data best; linear, quadratic or exponential? Explain.
The quadratic model is somewhat better than the exponential and linear equations. However all three fit the data well.
2. Sketch that curve onto the graph above.
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Predict World Population for the year 2005
3. Enter the regression equations into your graphing calculator. (Note: do not round off.) Go to the table scroll down to n= 55 = 2005. Record the predicted population for 2005.
Method
Predicted World
Population for 2005
Linear
Regression
6.36 billion
Quadratic
Regression
6.6425
Exponential
Regression
6.8581
4. The actual population for 2005 was 6,470,340,436. Compare this total with the predicted values from the above table. Which equation was closest?. Any surprises??
Yes! The linear model was the closest even though the LinReg model had the weakest correlation of 0.9955 vs. 0.998 for ExpReg and 0.9988 for QuadReg.
Predict World Population for the year 2050
5. This time go to the table scroll down to n = 100 = 2050 and record the predicted population for 2050.
Method Linear
Regression
Quadratic
Regression
Exponential
Regression
Predicted World
Population for 2050
9.6356 billion 11.942 billion 15.285 billion
6. How old will you be in the year 2050? ___ Age +_______ = _____
7. Which population prediction do you think is most accurate?
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9.6356 Billion via LinReg
8. How much will the world population have increased since 2005?
Population Change: ___ 3.2756 billion _______________
Percent increase in Population: _____ 51.5 % increase ______________
3.2756 = 0.515
6.36
9. Do you feel that the planet can sustain the predicted world population in
2050? Please share your thoughts. Please write in complete sentences.
Answers will vary
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Teacher Key
Name: ____________________________ Class Period:______________
When studying population growth and sustainability it is important to be acquainted with how the world’s population is distributed today. In this problem you will;
First:
Third:
Fourth:
Make a pie chart to illustrate world population distribution in the year 2008.
Second: Use historical growth data to predict the world population for the year 2050.
Make a new pie chart illustrating the projected world population distribution in the year 2050.
Compare and contrast the 2005 World Population pie chart with the 2050 World Population pie chart
1. Using continental population data from the U.S. Census International Data
Base.
A. Calculate the world population total. 6,706,992,932
B. Calculate the percent of total for each continent. Continental Population
6,706,992,932
C. Calculate the size of the pie slice for each continent. Answer in B *360
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Continent
Africa
Asia
Europe
Oceania
North America
South America
Population 2008 Percent of Total Slice (sector) size
972,752,366
4,053,868,153
729,553,228
34,368,042
527,831,687
388,619,456
0.145 = 14.5%
0.604 = 60.4%
0.079 = 7.9%
0.058 = 5.8%
52º
218º
0.109 = 10.9% 39º
0.005 = 0.5% 2º
28º
21º
2.
Create your pie charts on the first circle below. Use a protractor to approximate each slice. ‘Fudging’ a little is OK. Be sure to give your graph a title and label each sector.
3. The annual population growth rates (in percent) for each continent during the years 2000 to 2005 were: Africa: 2.2%, Asia: 1.2%, Europe: 0%, Oceania:
1.3%, North America: 1.0%, and South America 1.4%. (Statistical Yearbook
2007; Statistics Norway)
Use the exponential growth formula to find the expected continental population for the year 2050. Record your results in the chart below.
2050 Population = (2008 population)(1 + r) t r = rate of population growth (2.2% = .022) t = the number of years from 2008 until 2050
Example: AFRICA 2050 Population = (972,752,366)(1.022) 42
= 2,426,274,419 people
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Continent Growth rate (r)
Projected
Population 2050
(millions)
2.2% 2,426,274,419
Percent of
Total
Slice (sector) size
Africa
Asia 1.2% 6,690,385,536
Europe
Oceania
0%
1.3%
729,553,228
59,122,323
North America 1.0% 801,665,432
0.213
=21.3%
0.587
=58.7%
77º
211º
0.064 =6.4% 23º
0.005 =0.5% 2º
0.070 =7.0% 25º
South America 1.4% 696,816,858
TOTALS 11,403,817,798
0.061 =6.1% 22º
100% 360º
After calculating total world population, find the values for columns 4 and 5.
4. Create a second pie chart in the space below. Be sure to give the graphs a title and label each sector.
World Population by Continent
2008
1
2
3
4
5
6
Africa
Asia
Europe
Oceanla
North
America
South
America
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2050
1
2
Africa
Asia
3
Europe
4
Oceania
5 North America
6
South
5. Which continent experienced the greatest increase in population growth?
Asia has the greatest increase. Its population increased by 2,636,000,000
6. Which continent experienced the greatest percent increase in population?
Africa experienced the greatest percent increase of almost 60%
7. Given a continuation of current growth rates, will Africa’s population ever exceed
Asia’s population? Explain?
Yes, because Africa has an exponential growth rate that is greater than Africa’s. Africa’s population will exceed China’s in 146 years at current growth rates.(approximately)
8. Given a continuation of current growth rates, will North America’s population ever exceed Africa’s population? Explain?
No, North America’s population is growing at a slower exponential rate than
Africa’s population. The population of North America will always be less.
9. Use the table on your graphing calculator to determine how long it will take for
North America’s population to exceed the population of Europe.
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In approximately 33 years North America’s population will exceed Europe’s
Spreadsheet Calculations
2008 Population % of total pie slice
972,752,366 0.145035544 52.21279571
4,053,868,153 0.604424098 217.5926753
729,553,228 0.108775011 39.15900386
34,368,042 0.00512421 1.844715694
527,831,687 0.078698709 28.33153535
388,619,456 0.057942428 20.85927413
6,706,992,932
5yr growth r
1.022
1.012
1
1.013
1.01
1.014
2008 Population r^42
2050
Population % of Total Pie slice
972,752,366 2.494236461 2426274419 0.212759837 76.59354142
4,053,868,153 1.650370778 6690385536 0.586679448 211.2046014
729,553,228 1 729553228 0.063974472 23.0308101
34,368,042 1.720270354 59122323.79 0.005184433 1.866395705
527,831,687 1.518789895 801665432.3 0.070297987 25.30727523
388,619,456 1.793057059 696816858.7 0.061103823 21.99737611
11403817798
6,706,992,932
2050 - 2008 % change
1,453,522,053 0.599075703
2,636,517,383 0.394075553
0 0
24,754,282 0.418696022
273,833,745 0.341581081
308,197,403 0.442293264
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From http://www.infoforhealth.org/pr/m15edsum.shtml
Most developed economies currently consume resources much faster than they can regenerate. Most developing countries with rapid population growth face the urgent need to improve living standards. As we humans exploit nature to meet present needs, are we destroying resources needed for the future?
In the past decade in every environmental sector, conditions have either failed to improve, or they are worsening:
Public health.
Unclean water, along with poor sanitation, kills over 12 million people each year, most in developing countries. Air pollution kills nearly 3 million more. Heavy metals and other contaminants also cause widespread health problems.
Food supply.
Will there be enough food to go around? In 64 of 105 developing countries studied by the
UN Food and Agriculture Organization, the population has been growing faster than food supplies.
Population pressures have degraded some 2 billion hectares of arable land—an area the size of Canada and the US.
Freshwater.
The supply of freshwater is finite, but demand is soaring as population grows and use per capita rises. By 2025, when world population is projected to be 8 billion,48 countries containing 3 billion people will face shortages.
Coastlines and oceans.
Half of all coastal ecosystems are pressured by high population densities and urban development. A tide of pollution is rising in the world's seas. Ocean fisheries are being overexploited, and fish catches are down.
Forests.
Nearly half of the world's original forest cover has been lost, and each year another 16 million hectares are cut, bulldozed, or burned. Forests provide over US$400 billion to the world economy annually and are vital to maintaining healthy ecosystems. Yet, current demand for forest products may exceed the limit of sustainable consumption by 25%.
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Biodiversity.
The earth's biological diversity is crucial to the continued vitality of agriculture and medicine—and perhaps even to life on earth itself. Yet human activities are pushing many thousands of plant and animal species into extinction. Two of every three species is estimated to be in decline.
Global climate change.
The earth's surface is warming due to greenhouse gas emissions, largely from burning fossil fuels. If the global temperature rises as projected, sea levels would rise by several meters, causing widespread flooding. Global warming also could cause droughts and disrupt agriculture.
How people preserve or abuse the environment could largely determine whether living standards improve or deteriorate. Growing human numbers, urban expansion, and resource exploitation do not bode well for the future. Without practicing sustainable development, humanity faces a deteriorating environment and may even invite ecological disaster.
Taking action.
Many steps toward sustainability can be taken today. These include using energy more efficiently; managing cities better; phasing out subsidies that encourage waste; managing water resources and protecting freshwater sources; harvesting forest products rather than destroying forests; preserving arable land and increasing food production through a second Green Revolution; managing coastal zones and ocean fisheries; protecting biodiversity hotspots; and adopting an international convention on climate change.
Stabilizing population.
While population growth has slowed, the absolute number of people continues to increase—by about 1 billion every 13 years. Slowing population growth would help improve living standards and would buy time to protect natural resources. In the long run, to sustain higher living standards, world population size must stabilize
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It's an old question. Two hundred years ago, Thomas Malthus said population would race ahead of food supply, but he wasn't the first. The early Christian writer Tertullian said (around AD 200, in De Anima):
"We are burdensome to the world, the resources are scarcely adequate for us... Truly, pestilence and hunger and war and flood must be considered as a remedy for nations, like a pruning of the human race becoming excessive in numbers."
That was when the population of the whole planet was maybe 100 million or so. We reached the first billion mark by about 1850. By 1950, it was about 2.5 billion. In less than one short lifetime, this figure doubled. It passed six billion in the late 1990s. Note that: humans took 150,000 years to get to the first billion. The most recent billion arrived in just 12 years.
Nobody knows how many people the planet could hold. The UN predicted this week that fertility would decline and longevity would increase until the global population stabilized at nine billion in 2300. Some optimists have argued that the planet could support 1,000 billion; others look at what is happening right now and wish that it had stayed at ancient Roman levels.
Joel Cohen, the Rockefeller University population biologist, argues in a 1995 book (How Many People can the
Earth Support?) that it isn't a question like "How old are you?" which only has one answer at any one time.
Cohen argues that you could fit one billion people each a metre apart, into a field 32km square. So everybody in the world would fit easily into Yorkshire. But it takes 900 tonnes of water to grow a tonne of wheat, and there is only so much water, so much land and so much sunshine. Human action has its own "ecological footprint"; there has to be so much land to provide food, clothing, shelter, medicines, building material, fresh air and clean water for any one human. It takes, according to some calculations, 2.1 hectares of land and water to provide for one average human. The important word is: average. The American footprint is about 10 hectares. So if all humans lived at US standards, we'd need another four Earths
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