What is the formula used to represent an exponential relationship?

The formula ( y = cb^x ) represents an exponential relationship, where ( c ) is a constant that represents the initial value or y-intercept, and ( b ) is the base of the exponential function that indicates the rate of growth or decay. In this context, ( x ) is the independent variable, and as ( x ) increases, ( y ) changes at an increasing rate if ( b > 1 ) (indicating growth) or at a decreasing rate if ( 0 < b < 1 ) (indicating decay).

This type of equation is fundamental in various applications, including modeling population growth, radioactive decay, and financial investments, where quantities change at rates proportional to their current value. Thus, the presence of the exponent indicates that the relationship exhibits the characteristics typical of exponential change, distinguishing it from linear or polynomial relationships, as seen in the other options provided.