Question

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

distance over time
\

$$\begin{tabular}{|c|c|} \\hline time (minutes) & distance (miles) \\\\ \\hline 0 & 0 \\\\ \\hline 5 & 4 \\\\ \\hline 10 & 9 \\\\ \\hline 15 & 13 \\\\ \\hline 30 & 18 \\\\ \\hline \\end{tabular}$$

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

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

Explanation:

Identify the domain of the given data

Using the Linear Modeling knowledge point
The independent variable is Time (minutes). The data points given in the table are:

• \(t = 0\)
• \(t = 5\)
• \(t = 10\)
• \(t = 15\)
• \(t = 30\)

The minimum time value in the dataset is \(0\) minutes, and the maximum time value is \(30\) minutes.

Define interpolation

Interpolation refers to making a prediction for an unknown value that lies within the range of the observed data points.
Since the observed time values range from \(0\) to \(30\) minutes, any prediction made for a time \(t\) such that \(0 \le t \le 30\) is considered interpolation.

Determine the correct interval

The entire interval over which she would be interpolating is from the minimum observed independent variable value to the maximum observed independent variable value.
This corresponds to the range from \(0\) to \(30\) minutes.

Answer:

• 0 to 18 minutes
• 0 to 5 minutes
• 0 to 30 minutes (Correct answer)
• 18 to 30 minutes