Let's analyze the details provided by the table and deduce which statements are true.
1. The independent variable is the number of people.
This statement is true. In the given table, the number of people is the variable that changes independently (values 6, 9, 12, 15), and it affects the dependent variable, which is the total cost.
2. The initial value (initial fee) for the picnic is \[tex]$40.
This statement is true. The initial value, which can be interpreted as the y-intercept of the linear function, is \$[/tex]40.
3. The rate of change is \[tex]$8.67 per person.
This statement is false. The rate of change, or slope of the linear function, is \$[/tex]2.00 per person.
4. As the number of people increases, the total cost of the picnic increases.
This statement is true. Since the relationship between the number of people and the total cost is linear with a positive slope, as the number of people increases, the total cost also increases.
5. If 4 people attended the picnic, the total cost would be \[tex]$46.
This statement is false. If 4 people attended the picnic, given the linear relationship derived from the table, the total cost would be \$[/tex]48.
To summarize, the true statements are:
- The independent variable is the number of people.
- The initial value (initial fee) for the picnic is \$40.
- As the number of people increases, the total cost of the picnic increases.
