The equation y = a \cdot b^x represents an exponential function, where y is the output, a is a constant that determines the initial value, b is the base that indicates the growth or decay rate, and x is the exponent. If b > 1 , the function shows exponential growth, while if 0 < b < 1 , it indicates exponential decay. Exponential functions are commonly used in various fields, such as finance for compound interest calculations, biology for population growth models, and physics for radioactive decay. Understanding this equation helps in analyzing how quantities change over time.