What is exponential growth?

What is exponential growth? Whenever something is increasing or growing rapidly as a result of a constant rate of growth applied to it, that thing is experiencing exponential growth.

The figure below is an example of exponential growth. In fact, it is the graph of the exponential function y  = 2x

The general form of an exponential function is y = abx. Therefore, when y = 2x, a = 1 and b = 2.

The following table shows some points that you could have used to graph this exponential growth. Try to locate some of these points on the graph!

Exponential growth
x 2x y
1 21 2
2 22 4
3 23 8
0 20 1
-1 2-1 1/2 = 0.5
-2 2-2 1/4 = 0.25
-3 2-3 1/8 = 0.125

What is exponential growth in real-life?

There are many real-life examples of exponential growth. For example, suppose that the population of Florida was 16 million in 2000. Then every year after that, the population has grown by 2%. This is an example of exponential growth.

Notice that the rate of growth is 2% or 0.02 and it is constant. This is important since the rate of growth cannot change.

Let us find the exponential function.

Year 2001 or 1 year after: 

16,000,000 + 16,000,000 x 0.02  = 16,000,000 (1 + 0.02 )

16,000,000 + 16,000,000 x 0.02  = 16,000,000(1.02)     

16,000,000 + 16,000,000 x 0.02  = 16,000,000(1.02)1

Year 2002 or 2 years after:

16,000,000(1.02) + 16,000,000(1.02) x 0.02 = 16,000,000(1.02) [1 + 0.02]

16,000,000(1.02) + 16,000,000(1.02) x 0.02 = 16,000,000(1.02)(1.02)

16,000,000(1.02) + 16,000,000(1.02) x 0.02 = 16,000,000(1.02)2

Following this pattern, suppose that

  • x is the number of years since 2000
  • 16,000,000 is the starting amount
  • 1.02 is the rate or growth factor

Then y = 16,000,000(1.02)x

Comparing this exponential function with y = abx, we see that a = 16,000,000 and b = 1.02.

General rule for modeling exponential growth

Exponential growth can be modeled with the function

y = abx for a > 0 and b >1

y = abx

x is the exponent

a is the starting amount when x  = 0

b is the base, rate, or growth factor and it is a constant and it is greater than 1.

Recent Articles

  1. Box and Whiskers Plot

    Nov 18, 22 08:20 AM

    Easily learn to construct a box and whiskers plot for a set of data by using the median and the extreme values.

    Read More

  2. Binary Number System

    Nov 17, 22 10:53 AM

    This lesson will give you a deep and solid introduction to the binary number system.

    Read More

Tough algebra word problems

100 Tough Algebra Word Problems.

If you can solve these problems with no help, you must be a genius!

Math quizzes

 Recommended

Math vocabulary quizzes