To determine the amount of time it takes for the nail to reach the same orientation it had when it entered the tire, we need to identify a key feature of the function that describes the nail's position over time.
The data given is as follows:
[tex]\[
\begin{array}{|c|c|}
\hline
\text{Time} \ (s) & \text{Approximate height of the nail off the ground (inches)} \\
\hline
0 & 0 \\
\hline
0.01 & 2.1 \\
\hline
0.02 & 7.6 \\
\hline
0.03 & 14.9 \\
\hline
0.04 & 21.5 \\
\hline
0.05 & 25.5 \\
\hline
0.06 & 25.5 \\
\hline
0.07 & 21.5 \\
\hline
\end{array}
\][/tex]
Here, we're looking for a key feature of the function that would help us determine how long it takes for the nail to return to its starting orientation. The terms "minimum" and "maximum" refer to the lowest and highest points the nail reaches during one cycle, but they do not provide information about the time it takes for the nail to complete a cycle.
The term "period" refers to the amount of time it takes for the function to complete one full cycle and return to its initial value. This is the key feature that tells us the duration required for the nail to go through all its positions and come back to the same orientation it started with.
According to the data, the height of the nail returns to 21.5 inches at 0.07 seconds, indicating the start of a new cycle. Therefore, the period of this function is the total time it takes for the nail to return to its initial orientation and repeat the cycle.
Thus, the key feature that can be used to determine the amount of time it takes for the nail to return to its starting orientation is the period.
