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.

For example suppose that the population of Florida was 16 million in 2000. Then every year, 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(1.02)

                                                                                          = 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)(1.02)

                                                                     = 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

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.

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