1. **Problem Statement:** We want to match the correct graph to the story of folding a piece of paper multiple times. 2. **Understanding the problem:** - Each fold doubles the thickness of the paper. - Let $x$ be the number of folds. - Let $y$ be the thickness of the paper in inches. 3. **Mathematical model:** - Initial thickness is $y_0$ (usually very small, e.g., 0.01 inches). - After 1 fold, thickness is $2 \times y_0$. - After 2 folds, thickness is $2^2 \times y_0$. - After $x$ folds, thickness is $$y = y_0 \times 2^x$$ 4. **Explanation:** - The thickness grows exponentially with the number of folds. - This means the graph should show a curve that increases rapidly as $x$ increases. 5. **Matching graphs:** - Graph A: Linear increase then plateau then decrease — does not match exponential growth. - Graph B: Linear increase — does not match exponential growth. - Graph C: Decreasing curve — opposite of expected. - Graph D: Exponential or curving increase — matches the model. **Final answer:** The correct graph is **Graph D**. $$\boxed{y = y_0 \times 2^x}$$