From the graph in Question 28, we observe the following:

• The data points exhibit a non-linear decrease, with a sharper drop initially that levels off over time.
• This pattern aligns with an exponential decay trend, where the rate of decrease slows down as $x$ increases.

Conclusion:

An exponential model would be a better choice than a linear model to describe this data. The linear model assumes a constant rate of change, which is not the case here.

Would you like further clarification or have any questions about this?

Here are 5 related questions to expand your understanding:

1. How do you identify whether a trend fits a linear or exponential model?
2. Can you derive the equation of the exponential function from the given points?
3. What real-life scenarios follow an exponential decay model?
4. How does an exponential model differ from a logarithmic model in data fitting?
5. How would adding more data points impact the choice of the model?

Tip:

When analyzing data trends, always check the residuals (differences between observed and predicted values) after fitting a model. This helps verify if the chosen model is the most appropriate.