2. Exponential Astonishment
Discussion Paragraph 8B
1 web
59. National Growth Rates
60. World Population Growth
1 world
61. Doubling Time
62. Radioactive Half-Life
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3. Real Population Growth
Unit 8C
Real Population Growth
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4. Varying Growth Rate CN (1)
The average annual growth rate for world population since 1650 has been about .7%. However the annual rate has varied significantly. It peaked at about 2.1% during the 1960’s and is currently (as of 2009) about 1.2%.
1. Find the approximate doubling time for each of these growth rates.
A. .7%
B. 2.1%
C. 1.2%
Use each to predict world population in 2050 based on a 2009 population of 6.8 billion.

5. growth rate = birth rate – death rate
Definitions
Overall Growth Rate
The world population growth rate is the difference between the birth rate and the death rate:
growth rate = birth rate – death rate
For any particular species in a given environment, the carrying capacity is the maximum sustainable population—that is, the largest population the environment can support for extended periods of time.
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6. Birth and Death Rates CN (2)
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7. Logistic Growth Rate Logistic Growth Rate
A logistic growth model assumes that population growth gradually slows as the population approaches the carrying capacity.
When the population is small relative to the carrying capacity, logistic growth is exponential with a fractional growth rate close to the base growth rate, r.
Work through various scenarios with the students to see how the logistic formula behaves numerically, algebraically, and graphically.
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8. Exponential versus Logistic Growth
In the exponential case, the growth rate stays equal at all times. In the logistic case, the growth rate starts out equal and as time progress the growth rate becomes smaller, until it finally reaches zero as the population levels out at the carrying capacity.
The website has excellent population graphs that might be used to demonstrate some actual logistic growth for the world and/or individual nations.
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9. Are We Growing Logistically? CN (3)
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10. Overshoot and Collapse
The phenomenon where a real population increases beyond the carrying capacity in a relatively short period of time is overshoot. If the overshoot is substantial, a rapid and severe decrease in the population can occur—a phenomenon known as collapse.
The commentary in the practical matters Choosing Our Fate (page 495) is definitely worthy of class discussion.
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11. The Population of Egypt Case Study
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12. Difficulties of Population Prediction
The historical population of Egypt
This graph really puts the uncertainty of mathematical modeling for populations in proper perspective!
SOURCE: T.H. Hollingsworth, Historical Demography (Ithaca, NY: Cornell University Press, 1969).
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13. What is the Carrying Capacity?
Any estimate of carrying capacity is subject to great uncertainty, for at least four important reasons:
The carrying capacity depends on consumption of resources such as energy. However, different countries consume at different rates.
The carrying capacity depends on assumptions about the environmental impact of the average person. A larger average impact on the environment means a lower carrying capacity.
The carrying capacity can change with both human technology and the environment.
The earth is such a complex system that precisely predicting the carrying capacity may be impossible.
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14. Example
Suppose a country’s birth rate (per 1000) is 9.2 and its death rate (per 1000) is Determine the population growth rate.
Since the country’s death rate exceeds its birth rate, the population growth rate is negative. Thus, the population is decreasing.
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15. Example
Consider a population that begins growing exponentially at a base rate of 4.0% per year and then follows a logistic growth pattern. If the carrying capacity is 50 million, find the actual growth rate when the population is 5 million.
Solve the Logistic growth rate formula for r.
Use a growth rate of 4.0% = 0.04.
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16. Quick Quiz CN (5)
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17. Homework 8C Discussion Paragraph 8B Class Notes 1-5 P.498: 1-12 1 web
34. Population Predictions
35. Carrying Capacity
36. US Population Growth
37. Thomas Malthus
38. Extinction
1 world
39. Population Growth
40. Immigrations
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