An exponential function is a mathematical function of the form f(x) = a \cdot b^x , where a is a constant, b is the base (a positive number not equal to 1), and x is the exponent. These functions are characterized by their rapid growth or decay, depending on the value of b . For example, if b > 1 , the function grows quickly, while if 0 < b < 1 , it decreases rapidly. Exponential functions are widely 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 at rates proportional to their current value.