1. **State the problem:** We need to find a function $f(n)$ that models the geometric sequence given by the terms $9, 3, 1, \frac{1}{3}, \frac{1}{9}$ for $n=1,2,3,4,5$ respectively. 2. **Recall the formula for a geometric sequence:** $$a_n = a_1 \cdot r^{n-1}$$ where $a_1$ is the first term and $r$ is the common ratio. 3. **Find the common ratio $r$:** $$r = \frac{a_2}{a_1} = \frac{3}{9} = \frac{1}{3}$$ 4. **Write the function using the formula:** $$f(n) = 9 \cdot \left(\frac{1}{3}\right)^{n-1}$$ 5. **Simplify the function if possible:** The function is already simplified with integers and fractions. **Final answer:** $$f(n) = 9 \cdot \left(\frac{1}{3}\right)^{n-1}$$