Question

How do you know if an exponential function is increasing or decreasing $?$

Answer 1

To find out if an exponential function is increasing or decreasing:

Exponential functions have the general form:$y=f\left(x\right)=a^x$, where $a>0,a\ne 1$and $a$ is called the base of the exponential function and x is any real number.

Whether the exponential function is increasing or decreasing depends on the base and power of the base.

If the base $a>1$ and has positive exponent(i.e. $x>0$ then the exponential function is increasing.

If the base $0<a<1$ and has negative power then the function is decreasing.

For Example: Let the exponential function with the positive power be $y=e^x$ then the graph of $e^x$ is

Let another exponential function with negative power be $y=e^{-x}$ then the graph of $e^{-x}$ is

Hence, the increasing and decreasing nature of exponential functions can be found out by their sign of power.