1. **State the problem:** We are given a table of values for a function and need to determine if the function is linear or nonlinear. 2. **Recall the definition:** A function is linear if the rate of change (slope) between any two points is constant. 3. **Calculate the slope between points:** Between $(0,20)$ and $(16,8)$: $$m_1 = \frac{8 - 20}{16 - 0} = \frac{-12}{16} = -\frac{3}{4}$$ Between $(16,8)$ and $(20,0)$: $$m_2 = \frac{0 - 8}{20 - 16} = \frac{-8}{4} = -2$$ 4. **Compare slopes:** Since $m_1 = -\frac{3}{4}$ and $m_2 = -2$ are not equal, the rate of change is not constant. 5. **Conclusion:** The function is nonlinear because the slope between points changes. **Final answer:** The function is nonlinear.