This data set is best suited to which mathematical model?ALinearBExponentialCLogarithmic

To determine the best mathematical model for the given data set among linear, exponential, and logarithmic options, we need to consider the characteristics of each model and how they relate to the data trends.

1. Linear Model (Option A): This model is best suited for data that shows a constant rate of change, meaning that as one variable increases, the other variable increases by a consistent amount. It's often represented by the equation $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

2. Exponential Model (Option B): An exponential model is applicable when the rate of change of response (y) increases or decreases multiplicatively (e.g., doubling). This is represented by the equation $y = ab^x$, where $a$ is a constant, $b$ is the base of the exponential function, and $x$ is the independent variable.

3. Logarithmic Model (Option C): A logarithmic model is applicable for data that increases quickly at first and then levels off, where the growth rate decreases over time. It is represented as $y = a + b \ln(x)$, where $a$ and $b$ are constants.

Conclusion

To determine which model fits best, you'll need to analyze the data visually (using scatter plots) and statistically (using regression analysis). Look for patterns in the data; for instance, if the data points appear to form a straight line, a linear model would be appropriate. If the points show a rapid increase followed by a plateau, the logarithmic model may be better. An exponential model suits data that grows rapidly in a consistent manner.

Without the actual data, it is impossible to definitively state the best model, but selecting from options A, B, or C should be based on these characteristics. If you can provide more context or specific data, I could help narrow down the choice further.