First, let's analyze the data provided for the Pulaski County Ferris wheel from the table:
[tex]\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
t & 0 & 2 & 4 & 6 & 8 & 10 & 12 \\
\hline
P(t) & 2 & 17 & 47 & 62 & 47 & 17 & 2 \\
\hline
\end{array}
\][/tex]
The data reflects the height [tex]\( P(t) \)[/tex] of a person on the Pulaski County Ferris wheel at different times [tex]\( t \)[/tex]. We observe the following:
- At [tex]\( t = 0 \)[/tex], the height is 2 feet.
- As time increases, the height changes, reaching 62 feet at [tex]\( t = 6 \)[/tex] seconds.
- The height then decreases, returning to 2 feet at [tex]\( t = 12 \)[/tex] seconds, which means the position has returned to its starting point.
This suggests that one full revolution of the Pulaski County Ferris wheel is completed after 12 seconds, as the height pattern repeats itself starting from [tex]\( t = 0 \)[/tex] up to [tex]\( t = 12 \)[/tex].
Therefore, the Pulaski County Ferris wheel takes 12 seconds to complete one full revolution.
Regarding the Mason County Ferris wheel, no data or information is provided to determine its revolution time. Hence, we cannot compare the revolution times of the two Ferris wheels.
Given the information:
- The Pulaski County Ferris wheel completes a full revolution in 12 seconds.
- We do not have data for the Mason County Ferris wheel.
We conclude that it cannot be determined from the given information which Ferris wheel takes a longer amount of time to complete one full revolution.
