1. **State the problem:** We have data showing the number of candies $x$ dropped into a bottle and the resulting height $y$ of the soda geyser in feet. 2. **Given data:** \begin{align*} & (1, 2), (5, 9), (10, 12), (15, 14), (20, 15) \end{align*} 3. **Observation:** The height $y$ increases as $x$ increases, but the rate of increase slows down (increases at a decreasing rate). 4. **Function types to consider:** - Linear: $y = mx + b$ (constant rate of change) - Quadratic: $y = ax^2 + bx + c$ (rate of change changes linearly) - Logarithmic: $y = a \ln(x) + b$ (increases quickly at first, then slows down) - Exponential: $y = a b^x$ (increases at an increasing rate) 5. **Analyze the pattern:** - The height increases but the increments get smaller: from 2 to 9 (+7), 9 to 12 (+3), 12 to 14 (+2), 14 to 15 (+1). - This suggests the rate of increase is decreasing. 6. **Conclusion:** The function that models an increase at a decreasing rate is a logarithmic function. **Final answer:** C. a logarithmic function