Solution:
Given:
[tex]f(x)=9(\frac{1}{7})^x[/tex]The equation given is an exponential function.
An exponential function is of the form,
[tex]\begin{gathered} y=ab^x \\ \\ when\text{ }b>1,\text{ it represents an increasing function} \\ b<1,\text{ it represents a decreasing function} \end{gathered}[/tex]Hence, for the equation;
[tex]\begin{gathered} f(x)=9(\frac{1}{7})^x \\ b=\frac{1}{7} \\ b<1 \\ Hence,\text{ the equation is decreasing} \end{gathered}[/tex]Also, the graph is shown indicating a decreasing function.
Therefore, the answer is decreasing.
