1. **State the problem:** We are given four data points that suggest an exponential decay pattern: 16,510.34, 13,266.81, 10,778.49, and 8,774.27. 2. **Identify the exponential function form:** An exponential function can be written as $$y = ab^x$$ where $a$ is the initial value and $b$ is the base or common ratio. 3. **Calculate the common ratio $b$:** To find $b$, divide each term by the previous term: $$b_1 = \frac{13,266.81}{16,510.34} \approx 0.8035$$ $$b_2 = \frac{10,778.49}{13,266.81} \approx 0.8121$$ $$b_3 = \frac{8,774.27}{10,778.49} \approx 0.8140$$ 4. **Average the common ratios:** $$b = \frac{0.8035 + 0.8121 + 0.8140}{3} = \frac{2.4296}{3} \approx 0.81$$ 5. **Determine the initial value $a$:** The first value corresponds to $x=0$, so $$a = 16,510.34$$ 6. **Write the exponential function:** $$y = 16,510.34 \times 0.81^x$$ 7. **Interpretation:** This function models the data well, showing a decay by about 19% each step. **Final answer:** $$\boxed{y = 16,510.34 \times 0.81^x}$$