Question

georgianna wants to use the linear model associated with the data in the table to make a prediction.
distance over time

time (minutes)	distance (miles)
5	4
10	9
15	13
30	18

which range of time values describes the entire interval over which she would be interpolating?

• 0 to 5 minutes
• 0 to 18 minutes
• 0 to 30 minutes
• 18 to 30 minutes

Explanation:

Step1: Recall Interpolation Definition

Interpolation uses known data points (within the dataset's time range) to predict. The time values in the table are 0, 5, 10, 15, 30 minutes. The interval for interpolation is between the minimum and maximum known time values (excluding extrapolation).

Step2: Identify Known Time Range

The minimum time is 0 minutes, and the maximum time from the table (excluding extrapolation beyond known points) for interpolation is up to 30 minutes? Wait, no—wait, the known time points are 0, 5, 10, 15, 30. Wait, no, interpolation is between the smallest and largest time in the dataset? Wait, no, interpolation is estimating within the range of existing data. Wait, the time values in the table are 0, 5, 10, 15, 30. Wait, but 18 is not a data point. Wait, the question is about the interval over which she would be interpolating. Wait, the data has time from 0 to 30 minutes (the time values are 0,5,10,15,30). Wait, but the options: 0 to 30 minutes? Wait, no, wait the data points are at 0,5,10,15,30. So the entire interval for interpolation is between the minimum (0) and maximum (30) time values in the dataset, because interpolation is within the range of the known data. Wait, but let's check the options. The options are 0-5, 0-18, 0-30, 18-30. Wait, the time values in the table are 0,5,10,15,30. So the range of time values for interpolation is from the smallest time (0) to the largest time (30) in the dataset, because interpolation is estimating between existing data points. So the entire interval for interpolation is 0 to 30 minutes? Wait, no, wait: interpolation is between the minimum and maximum x-values (time) of the dataset. The x-values (time) are 0,5,10,15,30. So the minimum is 0, maximum is 30. So the interval for interpolation is 0 to 30 minutes. Wait, but let's confirm: interpolation is predicting within the range of the data, extrapolation is beyond. So the known time range is 0 to 30 minutes (since 30 is the largest time in the table). So the entire interval for interpolation is 0 to 30 minutes. Wait, but let's check the options. Option C is 0 to 30 minutes. Wait, but wait, the data points are at 0,5,10,15,30. So the time values in the table are 0,5,10,15,30. So the range of time for interpolation is from 0 (min) to 30 (max) minutes. So the correct option is 0 to 30 minutes.

Answer:

0 to 30 minutes (Option: 0 to 30 minutes)