All resource usage and/or pollution will grow exponentially but with different couplings to the population growth this is extremely relevant to greenhouse gas emissions which we will discuss later. For instance, the the previous "lecture" we learned that electricity generation scales as the population growth to the 3.5 power!

Returning to the theme of the very first "lecture in this class" regarding objectivity and science:

• In general, decision making is done at the self-interest level. With exponential resource usage, such decision making is extremely destructive. What we need is convergence on the least "bad" option.

  The ability to discern amoung the least bad alternatives is extremely difficult. Politics and pseudo-experts come into play. Science can help, but still the process is quite inexact.

• The self-interest decision making is encouraged because we do a very bad job at "training" and educating people to look at the data. We do an even worse job at presenting the raw data for objective analysis. Instead, we are a nation and community of SPIN doctors. This causes people to argue from a position of belief rather than a position of knowledge.

Now, of course, the problem is made worse by the perception that we are all afraid of math and that "formulas" don't apply to real life.

"Math, formulas and other things that don't apply to real life"

(--anonymous comment from student evaluation as the part they liked least about the course)

So we live in a society that is afraid of and doesn't understand numbers.

This again is a recipe for disaster as it means the public can be sold most anything

Clearly, Exponential growth, in general, is not understood by the lay public. If exponential use of a resource is not accounted for in planning - disaster can happen.

The difference between linear growth and exponential growth is astonishing. Exponential growth means that some quantity grows by a fixed percentage rate from one year to the next.

In this animation, one can clearly see that no matter what the growth rate is, exponential growth stars out being in a period of slow growth and then quickly changes over to rapid growth with a characteristic doubling time.

A handy formula for calculating the doubling time for exponential growth is:

So

• for n = 1% the doubling time is 70/1 = 70 years.
• for n =2% the doubling time is 70/2 = 35 years
• for n =5% the doubling time is 70/5 = 14 years
• for n = 35% the doubling time is 70/35 = 2 years

Its important to recognize that even in the slow growth period, the use of the resource is exponential. If you fail to realize that, you will run out of the resource pretty fast. The following table shows some resource exhaustion timescales done in the year 2000 given the growth rate at that time. Since 2000 some, but not all, of these rates have come down. Note that the exhaustion timescales do include recycling.

Material	Rate	Exhaustion Timescale
Aluminum	6.4%	2007 -- 2023
Coal	4.1%	2092 -- 2106
Cooper	4.6%	2001 -- 2020
Petroleum	3.9%	2011 -- 2023

A good example of poor public understanding.

A survey of Boulder Colorado residents about the optimal size for growth returned a result that most residents thought that a growth in population at the rate of 10% per year was desirable.

Well 10% a year may not seem innocuous but let's see how these numbers would add up?

• Year 1 60,000
• Year 2 66,000
• year 3 72,600
• Year 4 79,860
• Year 5 87,846
• Year 6 96,630
• year 7 106,294
• Year 8 116,923

So in 7 years (year 2--7) the population has almost doubled and by then 10,000 new residents per year are moving to Boulder!

If one had asked the question on the survey: Is it desireable for the population of Boulder to double in 7 years, there would have been an overwhelming NO. Clearly, the general population can not equate 10% growth rate with 7 year doubling time.

Note: There is some disagreement about the form of the population growth for the world. In population dynamics, most all species are subject to something called the logistic growth curve . It is unclear if that is the destined growth of human beings or not, as long as we are on the r-selected part of the logistic growth curve, population growth is exponential, characterized by a specific doubling time for that growth rate. There is no evidence in the data, yet, that we are on the flat portion of the logistic growth curve.

Example:

Number of Building Permits in Pasco WA

Growth Rate:

• initial value (1992) = 400
• final value (2000) = 1600
• ratio of final/inital = 4
• natural log (ln) 4 = 1.39
• over 9 years, growth rate is then 1.39/9 = 15.4% per year
• doubling time is 70/15.4 = 4.5 years (and the sample has doubled twice from 400 to 1600 in 9 years self consistent

• Population
• Energy resource use
• Number of shopping malls
• Number of automobiles on the freeway
• Number of Xerox Machines
• Rate of deforestation
• amount of paper used
• Internet usage

Clearly exponential rates of growth are an integral part of the planning process. Different aspects of a growing population have different exponential growth rates and these need to be considered.

For instance, suppose your urban area is growing at the rate of 5% a year. How does this translate into the following:

• Number of extra road miles that need to be built?
• Number of extra schools that need to be built (currently a problem in the Eugene Area)
• Price of housing and affordability of housing.
• zoning regulations
• amount of wetland mitigation to be done in the future
• growth of fire, police, sanitary and hospital services?
• The need to make reservations for campgrounds at State Parks?