Question

How is an exponential function created?
How can the properties of exponents help solve exponential equations?
What are some real-world applications for exponential functions?

Answer 1

What you need here is a definition. A exponential function is a function in which a variable appears in an exponent. It is NOT when a variable is raised to an exponent.

Not exponential: \(\large f(x)=x^\pi,\;f(y)= \sqrt y\)

Exponential: \(\large f(x)=\pi^x,\;f(y)= (\sqrt y)^{2y})\)

This is an important distinction.

For the rest you should do your own thinking.