Let's dive into the problem step-by-step to find the appropriate answers.
1. We have the number of visitors to a state park over a span of nine years. Our task is to model this data with a specific type of function and use this model to predict the number of visitors for the next year (year 10).
2. After analyzing the data and fitting it with an appropriate model, the function that best describes this data was determined to be a linear function. This means that the relationship between the years and the number of visitors is best represented by a straight line.
3. Using this linear model to make a prediction for year 10, we find that the number of visitors expected is [tex]\(229.5000000004767\)[/tex].
4. With this prediction, we need to determine if the number of visitors next year will be more than 400. Since [tex]\(229.5000000004767\)[/tex] is less than 400, we can conclude that the state park management should plan for less than 400 visitors next year.
Thus, the complete statements should be:
The visitor data is best modeled by a linear function.
Based on the model, the state park management should plan for less than 400 visitors next year.
