The function f(x) = a \cdot b^x is an example of an exponential function, where a is a constant that represents the initial value, and b is the base that determines the growth or decay rate. If b > 1 , the function shows exponential growth, while if 0 < b < 1 , it represents exponential decay. The variable x is the exponent, which indicates how many times the base b is multiplied by itself. Exponential functions like f(x) = a \cdot b^x are commonly used in various fields, including finance for calculating compound interest, biology for modeling population growth, and physics for radioactive decay. Their unique properties make them essential for understanding processes that change rapidly over time.