nit 8 Quiz - FOrm A More \( ~ \) Across a horizontal distance of 25 feet, a roller coaster has a steep drop. The height of the roller coaster at the bottom of the drop is - 125 feet, compared to its height at the top of the drop. What is the average amount that the roller coaster's height changes over each horizontal foot? Select one:

The change in height is calculated as the difference between the bottom and the top of the drop. Let the height at the top be \( h_{\text{top}} \) and at the bottom be \( h_{\text{bottom}} \). Given: - \( h_{\text{bottom}} = -125 \) feet - \( h_{\text{top}} = 0 \) feet (since the bottom is measured relative to the top) - Horizontal distance \( = 25 \) feet 1. Compute the change in height: \[ \Delta h = h_{\text{bottom}} - h_{\text{top}} = -125 - 0 = -125 \text{ feet} \] 2. Calculate the average change per foot: \[ \text{Average change per foot} = \frac{\Delta h}{\text{Horizontal distance}} = \frac{-125}{25} = -5 \text{ feet per foot} \] Thus, the roller coaster's height changes by \(-5\) feet for each horizontal foot.