Definition: A function of the form
\[
y(x)=a^x,
\]
where $a$ ($a \neq 1)$ is a positive number, is called an exponential function with base $a$.
Remark: For $a=1$ we get the function $y(x)=1^x=1$ for all $x$.
Example: $y(x)=5^x$ is an example of an exponential function.
\[
y(x)=a^x,
\]
where $a$ ($a \neq 1)$ is a positive number, is called an exponential function with base $a$.
Remark: For $a=1$ we get the function $y(x)=1^x=1$ for all $x$.
Example: $y(x)=5^x$ is an example of an exponential function.