To solve the problem of finding the nearest meter difference in elevation between Stefano and the climber at 6 seconds, we need to follow these steps:
1. Identify the initial height of Stefano's location:
From the given table, at [tex]\( t = 0 \)[/tex] seconds, the height ([tex]\( h(0) \)[/tex]) is 10 meters. This is Stefano's position.
2. Identify the height of the sunglasses at [tex]\( t = 6 \)[/tex] seconds:
From the table, at [tex]\( t = 6 \)[/tex] seconds, the height ([tex]\( h(6) \)[/tex]) is -166.4 meters. This is the position of the climber, as the sunglasses just passed by them.
3. Calculate the difference in elevation:
The difference in elevation is calculated by subtracting the height of the climber from Stefano's initial height:
[tex]\[
\text{ElevationDifference} = h(0) - h(6)
\][/tex]
Substituting the known values:
[tex]\[
\text{ElevationDifference} = 10 - (-166.4) = 10 + 166.4 = 176.4 \text{ meters}
\][/tex]
4. Round the difference to the nearest meter:
When rounding 176.4 to the nearest meter, the result is:
[tex]\[
176 \text{ meters}
\][/tex]
Therefore, the nearest meter difference in elevation between Stefano and the climber is 176 meters. Hence, the correct answer is:
[tex]\[
\boxed{176 \text{ meters}}
\][/tex]
