2. Copyright © 2011 Pearson Education, Inc. Exponential Astonishment Discussion Paragraph 8B 1 web 59. National Growth Rates 60. World Population Growth 1 world 61. Doubling Time 62. Radioactive Half-Life

3. Copyright © 2011 Pearson Education, Inc. Slide 8-3 Unit 8C Real Population Growth

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. Slide 8-4

5. 8-C Copyright © 2011 Pearson Education, Inc. Slide 8-5 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.

6. 8-C Copyright © 2011 Pearson Education, Inc. Slide 8-6 What Determines the Growth Rate Example Suppose a country’s birth rate (per 1000) is 9.2 and its death rate (per 1000) is 11.8. 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.

7. 8-C Birth and Death Rates CN (2) In 1950, the world birth rate was 3.7 births per 100 people and the world death rate was 2.0 deaths per 100 people. By 1975, the birth rate had fallen to 2.8 births per 100 people and the death rate to 1.1 deaths per 100 people. 2. Contrast the growth rates in 1950 and 1975. Copyright © 2011 Pearson Education, Inc. Slide 8-7

8. 8-C Copyright © 2011 Pearson Education, Inc. Slide 8-8 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. Logistic Growth Rate

9. 8-C Copyright © 2011 Pearson Education, Inc. Slide 8-9 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. Exponential versus Logistic Growth

10. 8-C Copyright © 2011 Pearson Education, Inc. Slide 8-10 Logistic Growth 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.

11. 8-C Are We Growing Logistically? CN (3a-b) Assume the earth’s carrying capacity is 12 billion people. Given that the population growth rate peaked in the 1960’s at about 2.1%, when the population was about 3 billion; a. Is it reasonable to assume that human population has been following a logistic growth pattern since the 1960s? b. Is it reasonable to assume that population has been growing logistically throughout the past century? Explain Copyright © 2011 Pearson Education, Inc. Slide 8-11

12. 8-C Copyright © 2011 Pearson Education, Inc. Slide 8-12 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. Overshoot and Collapse

13. 8-C Copyright © 2011 Pearson Education, Inc. Slide 8-13 What is the Carrying Capacity? 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. Any estimate of carrying capacity is subject to great uncertainty, for at least four important reasons:

14. 8-C The Population of Egypt Case Study One of the few cases for which long-term population data are available is that of Egypt. The graph uses an exponential vertical scale, with each tick mark representing a number twice as big as the previous one. Note the complexity of the pattern Mathematical models can be used to predict future changes only when the processes are relatively simple. Copyright © 2011 Pearson Education, Inc. Slide 8-14

15. 8-C Copyright © 2011 Pearson Education, Inc. Slide 8-15 SOURCE: T.H. Hollingsworth, Historical Demography (Ithaca, NY: Cornell University Press, 1969). The historical population of Egypt Difficulties of Population Prediction

16. 8-C Quick Quiz CN (5) Please answer the Quick Quiz multiple choice questions 1-10, starting on page 497. Copyright © 2011 Pearson Education, Inc. Slide 8-16

17. 8-C 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. Immigration Copyright © 2011 Pearson Education, Inc. Slide 8-17