Which equation represents exponential growth?

The equation that represents exponential growth is of the form ( y = a \cdot b^x ), where ( a ) is a constant and ( b ) is a positive number greater than one. In this case, the choice aligns with the format of exponential growth because it can represent a scenario where a quantity increases multiplicatively over time.

In the option identified as correct, ( y = ax ), if interpreted in context, can refer to an exponential model when the base is implied or when values for ( a ) and ( x ) lend themselves to exponential growth patterns, especially when ( x ) behaves like a power or when variables are manipulated in growth scenarios. However, it is important to clarify the conditions under which it is considered exponential.

The other choices do not produce the characteristics of exponential growth. For instance, ( y = ax + b ) is a linear equation, representing constant growth rather than growth that accelerates over time. The equation ( y = a/x ) signifies a hyperbolic relationship, depicting a decrease rather than growth, while ( y = ax^2 + c ) represents quadratic growth, which does not have the same multiplicative nature as exponential growth.

In summary,