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
Then y = 16,000,000(1.02)^{x}
General rule for modeling exponential growth
Exponential growth can be modeled with the function
y = ab^{x} for a > 0 and b >1
y = ab^{x}
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.
Nov 15, 18 05:01 PM
Modeling multiplication with number counters - Learning multiplication is fun!
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Nov 15, 18 05:01 PM
Modeling multiplication with number counters - Learning multiplication is fun!
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.