Thursday, November 1, 2012

Exponential Curve: A Sign of the Times

Dr. David R. ReaganPDFBy

Have you noticed how almost everything in life seems to be accelerating? Knowledge has exploded. We are traveling faster and farther than ever before. Instant, worldwide communication has become common place. And the power at our disposal is mind boggling.

The Bible teaches that this acceleration of life which we are experiencing will be a sign of the end times — a sign that will signal the soon return of the Lord.

Consider Daniel 12:4. In this verse the Lord tells Daniel that one of the signs of the end times will be an acceleration of travel and knowledge. Here's how the verse reads in the Living Bible paraphrase: "Daniel, keep this prophecy a secret... Seal it up so that it will not be understood until the end times when travel and education shall be vastly increased."

The same concept of end time acceleration is found in the New Testament. Jesus spoke about it when He talked with His disciples about the signs of the end times that would herald His return (Matthew 24:5ff). He mentioned a great variety of signs — spiritual, natural, societal and world political — and then He said these signs would be like "birth pangs" (Matthew 24:8).

Any mother knows that as the birth of a baby approaches, the birth pangs increase two ways. They increase in frequency and intensity. Thus, Jesus was saying that the closer we get to the time of His return, the more frequent and intense the signs will become. There will be more earthquakes and more intense ones. Likewise things like famine, pestilence and war will increase in frequency and intensity.

The Mathematical Concept

In mathematics this acceleration is called an "exponential curve." This term comes from what happens when rapid growth is plotted on a chart. When graphing the growth or decline of anything, the rate of change becomes exponential when it starts increasing or decreasing so fast that the plot line becomes vertical.

Now, the point is that the Bible indicates that the exponential curve will be one of the signs of the end times, and my thesis is that we are living in the midst of the exponential curve. Therefore, we are living in the end times.

Examples of the Curve

The 20th Century was the century of the exponential curve. Let's consider some examples.

1) Population — Demographers estimate that the population of the world at the time of Jesus was only 200 million.1 It took 1,650 years for the world's population to double! But thereafter it began to double very rapidly because the Industrial Revolution produced modern medicine, which, in turn, reduced infant mortality rates and increased longevity.

As the statistics below indicate, the rate of doubling has now reached exponential proportions.2

Time of Christ -- -- 200 million
1650 AD 1,650 years 400 million
1850 AD 200 years 1.3 billion
1950 AD 100 years 2.5 billion
1980 AD 30 years 4.5 billion
2000 AD 20 years 6.0 billion

Again, the key to this phenomenal growth has been modern medicine. Most people do not realize how modern our medicine really is and how radically it has affected our lives. For example, the life expectancy in the United States in 1900 was 47 years.3 At the end of the 20th Century it was 77 years. That's an increase of 30 years in life expectancy over a one hundred year period of time!

Many health problems today that are considered minor were deadly as recent as the 19th Century — appendicitis being a good example. During the horrible Flu Pandemic of World War I (1918-1919) over 40 million people died because the flu usually developed into pneumonia, and there was no guaranteed way for treating pneumonia. That's because the very first antibiotic, penicillin, was not discovered until 1928.4

Life before the 20th Century was short and brutal — often filled with suffering. If you are 35 years of age or older, you have lived longer than the vast majority of humanity.5 Here's an amazing fact: Two-thirds of all the people who have lived to the age of 65 are alive today!6

In the second segment of our exploration of the Exponential Curve, we'll look at more examples and consider the explosion of knowledge, transportation and communications.


1) The National Academies Press, "World Population Problems: The Growth of World Population,"

2) Worldmeters, "World Population Statistics,", pages 3-4.

3) Laura B. Shrestha, "Life Expectancy in the United States,", page 10.

4) Infoplace, "Medical Advances Timeline,", pages 1-4.

5) Michael D. Lemonick, "Working Stiffs," Time magazine, April 6, 1998, pages 60-61.

6) Edwin J. Pittock, "Is Living Longer More Than We Bargained For? America's Crisis in Aging," www.

1 comment:

Anonymous said...

The largest populations of the world are not in the most industrial areas of the world. India has one billion people. There is some other 'mystery' component going on here besides medicine etc.

PS. America has many infant deaths in the form of abortions