A data analyst is building a predictive model for company user growth using the exponential function $f(x) = a^x$. The system documentation states that the base, $a$, cannot be exactly equal to 1. Recalling the definition of an exponential function, what is the mathematical reason for this restriction?

An operations analyst is using the exponential function $f(x) = a^x$ to forecast inventory demand. In this model, the base $a$ is restricted from being 1 because setting the base to 1 results in a constant horizontal line ($f(x) = 1$) rather than a true exponential curve.

Mathematical Restriction on the Base of Exponential Models

A project manager is using the exponential function $f(x) = a^x$ to model the growth of a company's investment portfolio. Match each condition for the base $a$ with the resulting mathematical behavior of the function.

A technical writer is documenting the constraints for a graphing utility that models growth using the exponential function $f(x) = a^x$. To explain why the base $a$ is restricted from being the value 1, the writer outlines a logical proof. Arrange the following steps in the correct order to complete the explanation.