Chapter 4 - Exponential Functions - 4.2 Comparing Exponential and Linear Functions - Exercises and Problems for Section 4.2 - Exercises and Problems - Page 154: 17

$ f(x)=\frac{1}{2}\cdot\left(\frac{1}{3}\right)^x $

We want to have $f(x)=a b^{x}$. The graph shows that the points $(0,1/2),(3,1/54)$ lie on the curve of $f(x)$. We must have $f(0)=a b^{0}=a= \frac{1}{2}$ and so $f(x)= \frac{1}{2} b^{x}$. But $f(5)= \frac{1}{2} b^{3}= 1/54\implies b= (1/27)^{1/3}= 1/3 $ It follows that $$ f(x)=\frac{1}{2}\cdot\left(\frac{1}{3}\right)^x $$