Q. 12 - Precalculus Enhanced with Graphing Utilities

Question

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

If the graph of the exponential function $f\left(x\right)=a^x$, where $a>0$ and $a\ne 1$, is decreasing, then $a$ must be less
than ________.

Step-by-Step Solution

Answer

If the graph of the exponential function $f\left(x\right)=a^x$, where $a>0$ and $a\ne 1$, is decreasing, then $a$ must be less than one.

Step 1. Given

If the graph of the exponential function $f\left(x\right)=a^x$, where $a>0$ and $a\ne 1$, is decreasing, then $a$ must be less than ________.

Step 2. Find the point at which the function is decreasing

The exponential function $f\left(x\right)=a^x$ is a decreasing function when $0<a<1$

So $a$ must be less than one.