Exponential functions are mathematical functions that involve an exponent or power. There are two types of exponential functions: growth and decay.
1. Exponential Growth Functions: These functions have the form y = a*b^x, where a > 0 and b > 1. They model exponential growth, where the value of y increases rapidly as x increases. For example, the function y = 2^x is an exponential growth function, as the value of y doubles for each increase in x.
2. Exponential Decay Functions: These functions have the form y = a*b^x, where a > 0 and 0 < b < 1. They model exponential decay, where the value of y decreases rapidly as x increases. For example, the function y = (1/2)^x is an exponential decay function, as the value of y is halved for each increase in x.
Both types of exponential functions are important in many fields, including finance, biology, and physics. They are used to model phenomena such as compound interest, population growth, and radioactive decay.