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Lecture #5

Efficiencies and Growth Patterns

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Population with Respect to Time

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Population Growth

• Constant rate of increase leads to exponential growth

• Exponential growth has a portion that increases very quickly→ This is referred to as the knee of the graph

• The knee of the population graph appears to be around 1900

• Zooming in on that portion of the graph…

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Population Growth (cont’d)• 1830 = 1 billion• 1930 (100 years) = 2 billion• 1960 (30 years) = 3 billion• 1975 (15 years) = 4 billion• 1987 (12 years) = 5 billion• 1998 (11 years) = 6 billion

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Population Growth (cont’d)

• Every time there is a breakthrough (improved farming, clothing, medicine, technology) there is a jump in population

• This initial jump decreases until another breakthrough

• It is unknown when these jumps will occur

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Population Growth (cont’d)

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Energy Growth

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Energy Growth (cont’d)

• As people became more advanced they had the freedom to use energy more and have a better lifestyle

• The energy used to produce food has slightly increased

• The energy for houses & commerce, industry, and transportation has significantly increased

• The forms of energy used have also changed

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Energy Growth (cont’d)

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Energy Growth (cont’d)

• As different forms of energy were found, society adapted and used the newer forms

• The newer forms usually had advantages of:→ Cheaper at first, more efficient, more versatile, easier

to obtain, more abundant

• Total energy on a logarithmic scale (next graph)

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Energy Growth (cont)

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Demand

20% ROI

10% ROI

En

erg

y (Q

uad

s)

Time (years)

Energy Growth (cont’d)U.S. Energy Demand Versus Possible Supply from Solar Energy

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Energy Growth (cont’d)

• Even if the energy obtained from solar collectors grows by 10% it does not significantly increase (has not reached the knee of the curve)

• If solar energy obtained grows by 20% it becomes noticeable but does not account for the increase in energy needed

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Energy Growth (cont’d)

• Doubling time of U.S. energy use has been about 38 years

• Average ROI = 1.84%→1750 = 1 quad →1788 = 2 1 quad = 1,000,000,000,000,000 BTU→1826 = 4→1864 = 8→1902 = 16→1940 = 32→1978 = 64→2016 = 128→2054 = 256

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Growth Rates

• Growth rates are usually expressed as “Rate of Increase” (ROI)

• By knowing the ROI the “Doubling Period” can be determined, which is the amount of time needed for the value to double

• In Economics ROI = “Return on Investment” which means the same thing

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Growth Rates (cont)

• An approximate equation for Doubling Period is:→ Doubling Period = 70* years / (% growth

rate)

• For example:→ What is the doubling period if the world’s

population is increasing at 1.3%?→ Doubling Period = 70 years / 1.3 = 53.8

years

* Actually closer to 72

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Growth Rates (cont’d)

• Doubling with small numbers does not lead to a significant increase

• Doubling at large numbers grows extremely fast

• For example: → Beginning with 1 lily in a pond, and the

number of lilies doubles every day→ The pond can sustain 14,000 lilies→ How many days until there are 14,000 lilies?

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Lilies in Pond

Lilies in a Pond

(limit = 14,000 lilies)

Day Lilies

1 1

2 2

3 4

4 8

5 16

6 32

7 64

8 128

9 256

10 512

11 1024

12 2048

13 4096

14 8192

15 16,384

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Lilies in Pond - Graphical

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Growth Rates

What are the limiting agents that affect the growth of organisms?

→ Food Supply→ Energy Supply→ Space→ Pollution

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Growth Rates (cont’d)

What happens when organism growth becomes limited?

→ Expansion to new territories→ War→ Disease→ Death

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Growth Rates (cont’d)

• Hopefully technology breakthroughs will reduce or remove the limitations

→ Better food production techniques→ New energy sources→ Improved ways for using current energy

sources→ Improved medical procedures

• Uncertain when these will occur and in what areas (energy, food, medicine)

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Growth Rates (cont’d)

What are the signs that an energy resource is starting to limit growth?

→ Total “cost-of-use” becomes unacceptable (too expensive)

→ Government places restrictions on use