This section is meant for older children, Grade 6 and up, but it will also be of interest to most adults.

Most of what I am about to tell you is composed of selected excerpts from a lecture entitled "Arithmetic, Population and Energy" by Dr. Albert A. Bartlett, as well as lectures and articles by David Suzuki, Carl Sagan, and others. You can obtain the entire "Arithmetic, Population and Energy" lecture on video from the University of Colorado Boulder campus Bookstore. 1-800-255-9168. tradedesk@cubookstore.com.

As Professor Al Bartlett says at the beginning of his one-hour talk, "The greatest shortcoming of the human race is our inability to understand the exponential function."

If you read through these pages you will have a much better understanding of exponential growth. When you hear politicians and so-called "experts" try to tell you that we have nothing to worry about you will be able to calculate for yourself the accuracy of their comments.
                                ~Gran

Image credits for this page:
Gran: Jane Burkowski


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D O T H E M A T H - O U R P O P U L A T I O N G R O W T H R A T E I S U N S U S T A I N A B L E

Understanding world population and exponential growth

The earth does not contain enough resources to indefinitely sustain the current enormous population growth. In addition to depleting resources of food and water, overpopulation increases environmental problems.

Many people have heard the statement that the human population is growing exponentially, but few really understand what that means.

I am going to try to help you understand the exponential function. Don’t panic – it’s not that difficult.

First, let's clarify some terms:

The exponential function is used to describe the size of anything that grows steadily at a rate proportional to the current amount. When I say “grows steadily” I mean grows at a fixed rate – such as, for example, 5% per year.

Exponential growth describes the growth of a system in which the amount being added to the system is proportional to the amount already present: the bigger the system is, the greater the increase. If this sounds confusing, don't worry, you will understand it after we look at a few examples.

If we know something grows at 5% per year, we can calculate how long it will take to grow 100% - in other words, how long it will take to “double”. This is called the doubling time (DT).

We can calculate the “doubling time” using this fraction:
Dt=70 divided by the % growth per unit time. Thus a growth rate of 5% per year has a doubling time of DT=70 ÷ 5 = 14 years.

The number 70 comes from 100 multiplied by the natural logarithm of 2. If you wanted to know the tripling time you would use the natural logarithm of 3. You don’t need to remember where it came from, just remember that you use the number 70 when you are calculating “Doubling Time”.

So, if you see a news story that says things have been growing at a rate of 7% per year, that might not sound like much, but 70 divided by 7 is 10, so that means that whatever you are talking about doubles in 10 years.

...Let's look at some examples...