To analyze the visitor data and make predictions for next year, we'll follow these reasoning steps:
1. Modeling the Data:
- Based on the given visitor data for the last nine years:
[tex]\[
\begin{array}{|l|c|c|c|c|c|c|c|c|c|}
\hline
\text{Year} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 \\
\hline
\text{Visitors} & 452 & 360 & 348 & 302 & 198 & 124 & 204 & 308 & 398 \\
\hline
\end{array}
\][/tex]
- Our goal is to fit a mathematical model to this data to predict the number of visitors next year (year 10).
2. Choosing the Function Type:
- Various types of functions can be used for modeling data such as linear, quadratic, logarithmic, or exponential functions.
- In this case, after examining the trend and fitting models, the most suitable function that describes the data is a quadratic function.
3. Prediction for Next Year:
- Using the quadratic model, we calculate the predicted number of visitors for year 10.
- The model predicts that there would be approximately 484.62 visitors next year.
4. Planning for Visitors:
- Since 484.62 is greater than 400, the park management should plan for more than 400 visitors next year.
Therefore, the correct completions for the statements are:
The visitor data is best modeled by a quadratic function.
Based on the model, the state park management should plan for more than 400 visitors next year.
