To determine which mathematical model best fits the scatterplot, we can compare the \( R^2 \) values of the different models provided. The \( R^2 \) value indicates how well the model explains the variability of the data, with a value closer to 1 indicating a better fit.
The given \( R^2 \) values are:
- Linear regression: \( R^2 = 0.883 \)
- Quadratic regression: \( R^2 = 0.537 \)
- Exponential regression: \( R^2 = 0.492 \)
- Logarithmic regression: \( R^2 = 0.912 \)
Among these, the logarithmic regression has the highest \( R^2 \) value of 0.912, indicating it explains a greater amount of the variability in the data compared to the other models.
Therefore, the mathematical model that best fits the scatterplot is:
D) logarithmic model