Exponential Growth
See It in Action
Two examples of the idea done right—and one common look-alike that is not right.
EXAMPLE
EXAMPLE
NON-EXAMPLE
Definition
Exponential growth refers to a situation where the value of a quantity increases over time or as the independent variable (usually x) increases, following an exponential pattern. This occurs when the base of the exponential function is a positive number greater than 1 (i.e., b > 1).
An exponential growth function can be written in the general form:
Where:
a is the initial value (the starting amount when x = 0),
b is the base, which is a number greater than 1 for growth (the rate of increase),
x is the exponent (the input or time).
Key Characteristics of Exponential Growth:
The value of y increases as x increases.
As x becomes larger, y grows faster and faster.
The function shows rapid growth, especially as the value of x increases.
Example:
Consider the function y = 3 • 2^x:
The initial value is 3 (when x = 0, y = 3).
The base 2 means that the value of y doubles each time x increases by 1.
In summary, exponential growth describes how a quantity increases rapidly over time at a constant percentage rate.