To determine the range of time values over which we would be interpolating based on the given data, we need to understand the concept of interpolation. Interpolation involves estimating values within the range of the existing data points.
We are given the following table:
| Time (minutes) | Distance (miles) |
|----------------|------------------|
| 0 | 0 |
| 5 | 4 |
| 10 | 9 |
| 15 | 13 |
| 30 | 18 |
Here, the time values provided are 0, 5, 10, 15, and 30 minutes.
Interpolation can only be performed within the bounds of the given data. The smallest time value in the table is 0 minutes, and the largest time value is 30 minutes. Therefore, when you interpolate, you stay within these points' boundaries.
Given these observations, the correct choice for the range of time values that describes the entire interval over which she would be interpolating is:
0 to 30 minutes
This range includes all the provided data points and represents the full extent of the given data for interpolation purposes.
