The growth factor in an exponential function plays a pivotal role in determining the rate at which the function either increases or decreases.

In the context of an exponential function, the growth factor is represented by the base of the exponent. For instance, in the function

the variable $b$ denotes the growth factor. If $b > 1$, the function demonstrates exponential growth, indicating that the value of the function escalates rapidly as $x$ increases. On the other hand, if $0 < b < 1$, the function exhibits exponential decay, meaning that the value of the function diminishes swiftly as $x$ increases.

Grasping the concept of the growth factor is essential, as it enables us to predict how quickly quantities change over time. This is particularly relevant in real-life situations such as population growth, the spread of diseases, or compound interest in finance. By understanding the growth factor, one can accurately model and analyze these changes. Knowing the growth factor allows you to estimate how much a quantity will increase or decrease over a specified period.

In conclusion, the growth factor serves as a fundamental element of exponential functions, dictating the rate of change and facilitating our ability to model and comprehend various real-world phenomena effectively.