Section 8CSection 8CReal Population Real Population

GrowthGrowthpages 536 - 546pages 536 - 546

Population Growth PatternsPopulation Growth PatternsLinear Growth occurs when a population

increases by the same absolute amount in each unit of time.

Example: Straightown -- 500 each year

Exponential Growth occurs when a population increases by the same relative amount (same percentage) in each unit of time.

Example: Powertown: -- 5% each yearReal Population Growth assumes a

varying growth rate from year to year.

ex1/537 The average annual growth rate for world population since 1650 has been about 0.7%. However the annual rate has varied significantly. It peaked at about 2.1% during the 1960s and is currently (2006) about 1.2%.

a) Find the approximate doubling time for each of these growth rates.

b) Predict the world population in 2050

based on the 2000 population of 6.0 billion.

Doubling 70/0.7Times 70/2.1

70/1.2

Predicted 6E9 (1+.007)50

Populations: 6E9 (1+.021)50

6E9 (1+.012)50

23/544 Predict the world population in 2050 based on a 2000 population of 6.0 billion. Use the average annual growth rate between 1850 and 1950 which was about 0.9%.

25/544 Predict the world population in 2050 based on a 2000 population of 6.0 billion. Use the average annual growth rate between 1970 and 2000 which was about 1.6%.

Population Growth RatesPopulation Growth Rates

The world population growth rate is the difference between the birth rate and the death rate:

growth rate = birth rate – death rate

National population growth rates are more complicated. Why?

ex2/538 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 was 1.1 deaths per 100 people. Contrast the growth rates in 1950 and 1975.

1950: 3.7/100 – 2.0/100 = .017 = 1.7%

1975: 2.8/100 – 1.1/100 = .017 = 1.7%

Overall growth rates are the same.

29/545 Find Sweden’s net growth rate due to births and deaths (i.e. neglect immigration) in 1985, 1995 and 2003.

1985: 11.8/1000 – 11.3/1000 = .0005 = .05%

1995: 11.7/1000 – 11.0/1000 = .0007 = .07%

2003: 11.0/1000 – 10.0/1000 = .001 = 0.1%

Varying growth rates are most realistic!

Logistic Population GrowthLogistic Population Growthpg 539pg 539

Logistic Growth assumes that population growth gradually slows as the population approaches the carrying capacity (i.e. the maximum sustainable population).

The growth rate is given by:

populationgrowth rate = r x ( 1 - )

carrying capacity

where r is the base growth rate.

populationgrowth rate = r x ( 1 - )

carrying capacity

If the population is small, the growth rate is close to the base growth rate.

As the population grows, the growth rate becomes smaller.

If the population hits the carrying capacity, then growth rate is zero.

Exponential vs Logistic

0

2000

4000

6000

8000

10000

12000

0 50 100

year

popula

tion

exponential

logistic

S – shaped curve

Population approaches the carrying capacity and levels off.

31/545 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 60 million, find the actual growth rate when the population is 10 million, 30 million, and 50 million.

10 milliongrowth rate = .04 x ( 1 - )

60 million

30 milliongrowth rate = .04 x ( 1 - )

60 million

50 milliongrowth rate = .04 x ( 1 - )

60 million

Homework :Homework :

Pages 544-545Pages 544-545

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*Use EXACT formula based on given info.*Use EXACT formula based on given info.

Common Logarithms (page 531)

log10(x) is the power to which 10 must be raised to obtain x.

log10(x) recognizes x as a power of 10

log10(x) = y if and only if 10y = x

log10(1000) = 3 since 103 = 1000.

log10(10,000,000) = 7 since 107 = 10,000,000.

log10(1) = 0 since 100 = 1.

log10(0.1) = -1 since 10-1 = 0.1.

log10(30) = 1.4777 since 101.4777 = 30. [calculator]

Common Logarithms (page 505)

Practice with Logarithms (page 506)

13/506 100.928 is between 10 and 100.

15/506 10-5.2 is between 100,000 and 1,000,000.

17/506 is between 0 and 1.

19/506 log10(1,600,000) is between 6 and 7.

21/506 log10(0.25) is between 0 and 1.

10log ( )

Properties of Logarithms (page 531)

log10(10x) = x

log10(xy) = log10(x) + log10(y)

log10(ab) = b x log10(a)

10log ( )10 x x

Practice (page 533)

log10(x) is the power to which 10 must be raised to obtain x.

log10(x) recognizes x as a power of 10

log10(x) = y if and only if 10y = x

Properties of Logarithms (page 505)

Homework :Homework :

Page 533Page 533

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