Exponential functions
Definition
Exponential functions have the form f(x) = ab^x, where a and b are constants and b is greater than zero but not equal to 1. They grow or decay at a constant rate as x increases or decreases.
Analogy
Exponential functions are like compound interest in a bank account. The amount of money you have grows exponentially over time because the interest is continuously compounded based on a fixed rate.
Related terms
Growth factor: The value of b in an exponential function that determines how fast the function grows.
Decay factor: The reciprocal of the growth factor, representing how fast an exponential function decays.
Asymptote: A horizontal line that an exponential function approaches but never touches as x approaches positive or negative infinity.
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