The Exponential Curve

The Exponential Curve

Is it a sign that Jesus is returning soon?

By Dr. David R. Reagan

The Exponential Curve

[read in Lamplighter (pdf)]

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.

A Sign of the Times

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

2) Knowledge — Another area that is increasing exponentially is knowledge. The prophet Daniel was specifically told that knowledge would vastly increase in the end times (Daniel 12:4), and it has. In fact, we have become so overwhelmed with the flood of new information that it is difficult to find wisdom anymore, because wisdom comes from reflection on knowledge.


It is estimated that 80% of all scientists who have ever lived are alive today. Every minute they add 2,000 pages to man’s scientific knowledge, and the scientific material they produce every 24 hours would take one person five years to read.7 The scientific journals cannot publish all the academic articles that are being written. Many have to limit the articles to one page abstracts, and even then most articles are rejected for a lack of space.

Consider how rapidly knowledge is increasing:8

From Jesus to 1500 it doubled (1,500 years)
1500 to 1750 it doubled again (250 years)
1750 to 1900 it doubled again (150 years)
1900 to 1950 it doubled again (50 years)

Today, knowledge is doubling every 12 months!

That means encyclopedias are out of date before they can be printed, which is the reason they are no longer printed. Britannica stopped printing in 2010 after 244 years.9

I read recently where a research organization had determined that one Sunday issue of the New York Times contains more information than the normal person in the 19th Century was exposed to in a lifetime!10

The most amazing thing to me in the area of information is the World Wide Web that can be accessed through the Internet. Using it, I can access the documents of the Vatican in seconds, and then in a matter of moments, I can go to the Israel Museum in Jerusalem, or I can dart back to the Library of Congress in Washington, D.C. In short, I can access information all over the world without ever leaving my office.

3) Transportation — In 1900 the major means of transportation was what it had always been throughout history — namely, walking and riding a horse. The bicycle had been invented, and the steam engine had been applied to ships and trains. But steam powered transportation was too expensive for most people.

Below is a photograph of 5th Avenue in New York City in 1905. As you can see, the only means of transportation visible is the horse-drawn carriage.

New York City in 1905

I have a similar photo that was taken in my home town of Waco, Texas in 1912. It shows the city square, and like the photo above, all that can be seen are horse-drawn wagons and carriages.

Today we have automobiles (usually two or more to a family!) and airplanes. We have bullet trains that travel 150 miles per hour and planes that travel faster than the speed of sound. And then, of course, there are rocket ships that take astronauts into orbit around the earth.

In 1866 Mark Twain traveled to the Holy Land. It took him three months to get there. Today, a group can get on a jet plane in New York and be in Tel Aviv in 13 hours (and most will complain about how long the trip took!).

During the 19th Century, the average number of miles traveled per year by a person in the United States was 500. Many lived and died and never got outside the county they were born in! By 1900 the average number of miles traveled per year by a person inside the United States had risen to 1,000. Today it is 25,000 miles per year, and many of us put twice that much mileage on an automobile in a year’s time.

4) Communications — At the beginning of the 20th Century the telegraph had sped up communications considerably, and the telephone had been invented. But the fundamental means which most people used to get information was still the newspaper.

Today our communication resources are overwhelming. We have telephones, radio and television. We have exotic devices like fax machines, pagers and cellular phones. And we can communicate worldwide through satellites.

I never cease to be amazed when I see someone use a credit card at an Arab shop in the Old City of Jerusalem. The shop may be nothing but a primitive hole in the wall, but over in some dark corner there will be a machine where the merchant can swipe the card. A few moments later he receives an authorization. During those few moments, the card number has been transmitted to Tel Aviv, from Tel Aviv to New York by satellite, from New York to the credit card processing center somewhere in the States, and then back to the Arab shop in Jerusalem!

I am equally amazed at the way I can sit down at a computer at my home or office and use the Internet to send a letter in seconds to almost any place in the world. In 1995 when I got on the Internet, there were only 16 million people using it. Three years later, in 1998, there were 150 million. Today there are 2.2 billion users worldwide!11

Once again, we have the exponential curve.

5) Computers — Computer technology has contributed to the rapid acceleration of many aspects of life, and, of course, the exponential curve applies to the development of computers as well. Anyone who tries to stay on the cutting edge of what is new in computer equipment knows that it is a never-ending battle that requires a lot of money. Advances are so rapid that equipment is out of date within a few months.

IBM Sequoia

In 1970 I was a professor at a college where we bought an IBM computer for $100,000. It operated off punch cards, it was so large that it filled a room, and it generated so much heat that we had to have the room equipped with additional air conditioning. The computer’s memory was 64K!

Now, if you are not a computer buff, that may not mean much to you, but keep reading because I’m going to make it understandable; and in the process, I’m going to illustrate how rapidly computer technology has developed.

Ten years later in 1980, this ministry bought one of the first desktop computers made. It was a Tandy TRS 80, Model II. It cost $4,800 (equivalent to $12,500 today!). When I turned it on, I was astounded by the first thing that appeared on the screen: “64K Memory.” In ten years’ time we had gone from a computer that weighed more than a ton to one that sat on a desk top, and the price had dropped 95%. But the memory was the same!

Ten years later in 1990, I went to Radio Shack and bought an electronic Rolodex small enough to fit into the palm of my hand. It cost $90. And when I turned it on, guess what? The first message that appeared on the screen was “64K Memory.”

Today, you can purchase a computer with 4 gigs of memory and a 1 terabyte hard drive operating at 2.7 gigahertz for less than $500!

The exponential curve also applies to data storage units. The first floppy disk that we used in the TRS 80 was 8″ in size. It held 300,000 bytes of information. A few years later the 5 1/4″ disk appeared. It would hold 700,000 bytes. Then came the 3 1/2″ disk. Its capacity was 1.4 million bytes! The next hottest thing to come along was the CD Rom disk. I recently read an advertisement for a CD that contained 134,000 pages of theological documents — the equivalent of 1,400 pounds of books!

Today, my data storage device of choice is a tiny thumb drive or flash drive that holds 30 gigabytes!

6) Military Power — Throughout most of recorded history, the maximum power at man’s disposal consisted of bows and arrows, spears, and catapults. Even at the beginning of this century, war was still primitive. World War I turned into a stagnant war of attrition because neither side had sufficient power to break out of the trenches.

Eighty years later, we have air power, armored power, nuclear weapons, and sophisticated bacteriological and chemical weapons. We have ICBM’s that can deliver a nuclear payload halfway around the world. We have laser-guided missiles that can guide a bomb down a smoke stack hundreds of miles away. And we have nuclear submarines that can circle the globe without surfacing. Incredibly, just one of those subs today has more firepower than all the bombs dropped in World War II!12 It is no wonder the Bible says that in the end times “men will faint with fear” over the expectation of “the things which are coming upon the world” (Luke 21:26).

7) Violence — I don’t think I have to emphasize that violence and lawlessness have been increasing. But it is hard to comprehend how rapid the increase was during the 20th Century.

It is estimated by experts that the number of people killed in all the wars fought from the time of Jesus until 1900 was 40 million. In the 20th Century 231 million people died in wars, making it a century of unparalleled carnage.13

There are currently a total of 38 wars or civil wars raging worldwide.14 And then, of course, there has been the advent of international terrorism, resulting in the loss of tens of thousands of lives. In 2011 alone there were 10,283 terrorist attacks worldwide.15

Within the United States, violent crime increased 430% between 1960 and 2010. During the same period, the country’s population increased only 67%.16

8) Society — The disintegration of society has multiplied in speed as violence, wickedness and immorality have increased exponentially. Jesus prophesied this would happen when He said that end time society would be like it was in the days of Noah (Matthew 24:37-39), when violence and immorality prevailed (Genesis 6:11).

Paul prophesied about the disintegration of society in 2 Timothy 3:1-5 where he wrote that in the end times people would be lovers of self, lovers of money, and lovers of pleasure. The love of self is Humanism, and it is the religion of the world today, masquerading under many different labels. The love of money is Materialism, and money is the god of these times. The love of pleasure is Hedonism, and that is the prevalent lifestyle of today.

But God cannot be mocked or deceived. When a society makes Humanism its religion, Materialism its god, and Hedonism its lifestyle, there is always a payoff, and that is Nihilism, or despair. And thus it is no accident that we see societies around the world wallowing in despair.

I have witnessed the exponential decaying of society with my own eyes. I was born in 1938. When I was born:

  • Abortionists were sent to prison.
  • Pregnancy out of wedlock was thought of as scandalous.
  • Homosexuality was considered unnatural and immoral.
  • Pornography was despised as a perversion.
  • Marriage was sacred. Living together was taboo.
  • Divorce was a disgrace.
  • Homemaking was honored, and daycare was provided by mothers in their homes.
  • Child abuse was unheard of.
  • Ladies did not curse or smoke.
  • “Damn” was considered flagrant language in a movie. (A 1992 film called, “Glengarry Glen Ross,” had the “f-word” in it 138 times in 100 minutes!)17

I could go on and on about the many ways in which our society (and societies around the world) have decided to “call evil good and good evil” (Isaiah 5:20). But the most dramatic way I can think of to illustrate how rapid the deterioration of society has become in America is to consider the results of two polls concerning public school discipline problems, one taken in the 1940s and the other in the 1980s. Both were taken in the Fullerton, California School District. Consider the drastically different results (and weep!):

The Top Public School Discipline Problems:
(Source: Time Magazine, February 1, 1988)


  1. Talking
  2. Chewing gum
  3. Making noise
  4. Running in the halls
  5. Getting out of turn in line
  6. Wearing improper clothing
  7. Not putting paper in wastebaskets


  1. Drug Abuse
  2. Alcohol Abuse
  3. Pregnancy
  4. Suicide
  5. Rape
  6. Robbery
  7. Assault

9) Natural Disasters — The Bible says that natural disasters will also be increasing exponentially in the end times, and that is exactly what is happening.

Consider these statistics for natural disasters within our nation between October 1991 and November 2004, a period of 13 years:18

9 of the 10 largest insurance events in US history.
5 of the costliest hurricanes in US history.
3 of the 4 largest tornado swarms in US history.

And all that was before Hurricane Katrina in 2005!

Putting together all types of natural disasters worldwide, you can see on the chart below how rapidly they are increasing, from an average of 300 per year in the 1980s to almost 1,000 in 2010.

Weather Chart

Incidentally, this is a better way of considering natural disasters, as opposed to plotting individual types of disasters. That’s because one type of natural disaster can restrain another type.

Let me illustrate what I mean. Right now (2012) our nation is experiencing its worst drought in modern history, with over 61% of our nation affected.

But one side effect of the drought is that we are experiencing the lowest number of tornadoes in 60 years. After all, you can’t have tornadoes without thunderstorms. The drought has also greatly reduced the amount of flooding.

10) The Economy — This brings us to a man-made disaster — namely the out of control spending that has come to characterize the modern welfare state.

The exponential curve illustrated in the diagram below is leading to the destruction of our nation.


It took over 200 years for our nation’s debt to reach one trillion dollars in 1980. Thirty years later, in 2010, it had soared to 14 trillion. Today (2012), it has just topped 16 trillion. It is increasing at the rate of 75 million per hour. The interest alone is accumulating at the rate of 50 million an hour.19

A good way of illustrating the impact of this overwhelming debt is to consider how much it represents per person in the United States. At a Tea Party Rally in 2010, a little girl about 4 years old was seen wearing a sign that read: “I’m already $38,375 in debt, and I only own a doll house!” Since that time, our individual share has increased to $51,000.20

In short, our nation is bankrupt, and our economy could collapse any minute.

11) World Evangelism — Not all the exponential curves are bad. Modern technology has made it possible for the Gospel to be preached to billions of people through the use of such media as short wave radio, motion pictures, and satellite television.

And, again, this phenomenal development is a fulfillment of Bible prophecy. Jesus Himself said: “This gospel of the kingdom shall be preached in the whole world for a witness to all the nations and then the end shall come” (Matthew 24:14).

Consider translations of the Bible. In 1800 there were 71 in whole or in part. By 1930 that number had risen to 900. Today there are 2,100 with 1,900 in progress.21

Incidentally, those statistics are a little misleading because they leave the impression that many people still do not have a Bible in their language. The fact is that the existing translations cover over all the major languages of the world, representing more than 90% of the world’s population. The translations currently in progress are for tribal languages spoken by 100,000 or less people.

In March of 1995 Billy Graham broadcast a gospel message from Puerto Rico that was carried by 37 satellites to 185 countries and territories in a total of 117 different languages! Over 1.5 billion people viewed the program. It is estimated that more people heard that one sermon than had heard the Gospel since it was first proclaimed by the Apostle Peter 2,000 years ago!22

With regard to world mission activity, I attended a mission conference in the mid-1990s where one of the key speakers told us that 70% of all mission work in history had been done since 1900, and 70% of that since 1945, and 70% of that since 1985 — all due, of course, to the implementation of modern technology.23 The results have been overwhelming:

There were 10 million Christians in Africa in 1900.
Today: 516 million24

There were 700 thousand Christians in China in 1949.
Today: 70 million25

There were 50 thousand Evangelical Christians in Latin American in 1900.
Today: 60 million26

And, according to Muslim sources, every day 16,000 Muslims convert to Christianity, for a total of 6 million per year!27

Worldwide, the number of Christians has nearly quadrupled in the last 100 years, from about 600 million in 1910 to more than 2 billion in 2010, constituting one-third of the world’s population.28

The conversion rate is on the exponential curve:29

1800 – 100 per day
1900 – 1,000 per day
1950 – 4,000 per day
1980 – 20,000 per day
1990 – 86,000 per day
1995 – 100,000 per day
2010 – 175,000 per day

12) World Politics — The exponential curve also applies to world events. Habakkuk 1:5 is as relevant today as if it were written yesterday: “The Lord replied, ‘Look, and be amazed! You will be astounded at what I am about to do! For I am going to do something in your own lifetime that you will have to see to believe.'”

I took a Sabbatical in 1987 and wrote a book called Trusting God. Seven years later, in 1994, I took another Sabbatical and completely rewrote that book. The exercise gave me an opportunity to reflect back over the seven years between the two Sabbaticals. I was astounded — even overwhelmed — by the rapid and stupendous nature of world events.

Who could have dreamed in 1987 that within the next seven years any of the following events would have occurred? —

  • The tearing down of the Berlin Wall.
  • The peaceful liberation of Eastern Europe from Communism.
  • The collapse of the Soviet Union.
  • The reunification of Germany.
  • The resurgence of Islam and its emergence as the greatest threat to world peace.
  • The sending of 500,000 American troops to the other side of the world to defend a country most Americans had never heard of (Kuwait).
  • The handshake between Rabin and Arafat that has led to Israel surrendering portions of its heartland to the PLO.

In 1987 if you had predicted any of these developments, you would have been written off as “nuts.” The rapidity of these events and their radical nature is breathtaking. They underscore the possibility of the impossible. And they certainly reveal that man is not in control.

The Significance of the Curve

So, what does all this mean to you and me? I would mention at least three things.

First, the exponential curve is proof positive that Bible prophecy is true. The Lord has told us what He is going to do in the end times, and we had better pay attention to what He has said.

Second, the fulfillment of prophecy related to the exponential curve shows that God is in control. Even when it appears that everything on this earth is out of control, we can be assured that God is orchestrating all the chaos to the ultimate triumph of His Son in history (Psalm 2).

Third, the exponential curve is very strong evidence that we are living on borrowed time. It points to the fact that Jesus is at the very gates of Heaven, waiting for the command of His Father to return.

A Warning and an Illustration

I want to conclude by issuing a strong warning against taking time for granted.

Many people are doing that today. They are saying, “I’m going to get serious about the Lord when I get out of school;” or “after I get a job;” or “after I’m established in my career;” or “after I get married;” or “after I get my children raised.” Time is precious. There is very little left. Now is the time to get serious about the Lord.

Let me illustrate how critical the timing is by returning to the exponential curve. Suppose you put one bacterium in a jar, and assume it doubles every second. How many bacteria do you think would exist in the jar at the end of 30 seconds? The answer, incredibly, is 1,073,741,824. That’s more than a billion in thirty seconds! That’s the ferocity of the exponential curve.

Now, let’s carry the illustration a step further. If at the end of 30 seconds the jar is half full, how much longer will it take for the jar to become full? The answer is one second (because it will double in the next second). That is the suddenness of the exponential curve.

That’s what the Bible means when it says that people will be saying, “Peace and safety!” when “sudden destruction” will come upon them (1 Thessalonians 5:3).

A Call to Action

Are you taking time for granted? Don’t do it. The Exponential Curve is just one of many signs God is giving us to warn of the soon return of His Son. The Bible says that the only reason Jesus has not returned is because God does not wish that any should perish. 2 Peter 3:9 says:

The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance.

In other words, the lovingkindness of God has restrained Him from sending His Son back to this earth. But that restraint is soon coming to an end for our God is a God of justice, and as such, He must deal with the sinful rebellion of this world.

The signs of the times are shouting from the heavens that Jesus is returning soon to pour out the wrath of God on those who have rejected His love and grace. Are you ready for His return? Have you placed your faith in Jesus as your Lord and Savior? Do you understand that God deals with sin in only one of two ways?

Consider John 3:36: “He who believes in the Son has eternal life; but he who does not obey the Son shall not see life, but the wrath of God abides on him.”

Are you under grace or wrath? God deals with sin in one of those two ways. It is a glorious thing to be under the grace of God. It is a dreadful thing to be subject to His wrath.

Do not turn a deaf ear to the signs of the times. The time to act is now. If you are not a Christian, then reach out in faith and receive Jesus as your Lord and Savior. If you have already done that, then commit your life to holiness and evangelism.


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.

7) Seven-Minute Sermons, “Sustainable Knowledge at Work,”

8) “Knowledge Doubling,”

9) Julie Bosman, “After 244 Years, Encyclopaedia Britannica Stops the Presses,” The New York Times, March 13, 2012,

10) Oakton Community College 24/7 Library Research guide and Webletter, “Are You Information Savvy?”, page 1.

11) Sam Nurmi, “Internet 2011 in Numbers,”, page 4.

12) PBS, “Ship Guide: USS George Washington,”

13) Milton Leitenberg, “Deaths in Wars and Conflicts in the 20th Century,”, page 4.

14) Wikipedia, “List of Ongoing Military Conflicts,” conflicts, pages 1-4.

15) Haaretz, “Terrorist Attacks Drop Nearly 12% Worldwide in 2011, U.S. Report Shows,”

16) The Disaster Center, “United States Crime Rates 1960-2010,”

17) Brian Rentschler, “Review: Glengarry Glen Ross,” 385, page 3.

18) Robert Longley, “FEMA’s List of Top 10 U.S. Natural Disasters,”

19) “U.S. Debt Clock,”

20) Ibid.

21) Wycliffe Bible Translators, “The Worldwide Status of Bible Translation,” aspx.

22) Sherwood Eliot Wirt, “A Personal Look at Billy Graham,”, page 4.

23) From notes taken by the author.

24) Charles Colson, “How Christianity is Growing Around the World,”

25) Bible Probe, “The New Church: Miracles and Conversions China and More,” messages/414.html.

26) John L. Allen, Jr., “The Dramatic Growth of Evangelicals in Latin America,” National Catholic Reporter, August 18, 2006,

27) Ali Sina, “Islam in Fast Demise,”, page 1.

28) The Pew Forum, “Global Christianity: A Report on the Size and Distribution of the World’s Christian Population,”, page 1.

29) World Hopper Ministry Travel, “Facts About Missions,”

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