The image you've uploaded contains a table and describes the illumination of the Moon's surface during the first few days after a new moon. The data suggests that the Moon’s illumination increases over time, but the question at hand asks about the appropriateness of using a linear function to model this data.

To analyze this question:

• The illumination starts at 2% on day 1 and increases to 6% on day 2. By day 14, the illumination reaches 100%.
• Given this pattern, a linear function would assume that the rate of increase in illumination is constant over time.

However, the actual progression of illumination might not be perfectly linear because the Moon's illumination is based on its phase cycle, which is roughly 29.5 days. During the first few days of the cycle, the illumination tends to increase more gradually, and later on, it may increase at a different rate depending on the Moon's orbital geometry.

Thus, while a linear function might offer a reasonable approximation for short periods, it's likely less appropriate for modeling the full Moon's illumination across the entire cycle because it doesn't account for the natural nonlinear curve of the Moon's phases.

Would you like further details or have any additional questions on this topic?

Here are some related questions for further understanding:

1. How does the Moon’s illumination change over a full lunar cycle?
2. Why is the Moon’s illumination non-linear during the cycle?
3. What kind of function would more accurately represent the illumination of the Moon?
4. How can we use regression analysis to fit a model to this type of data?
5. What real-world phenomena exhibit similar non-linear patterns of change?

Tip: When modeling real-world phenomena like the Moon's phases, it's important to consider the nature of the underlying process, which in this case involves orbital mechanics and geometry.