Hence, the average rate of change in vertical height is:
-6
We know that the average amount that the roller coaster's height changes over each horizontal foot is basically the slope or the average rate of change of the height of the roller coaster to the horizontal distance.
i.e. it is the ratio of the vertical change i.e. the change in height of the roller coaster to the horizontal change.
Here the vertical change= -150 feet
and horizontal change = 25 feet
Hence,
Average rate of change is:
[tex]=\dfrac{-150}{25}\\\\=-6[/tex]
So, for every change in horizontal distance by 1 feet the vertical height drop by 6 feet.
Answer:
The average amount that the roller coaster's height changes over each horizontal foot is -6.
Further explanation:
The rate of linear function is known as the slope. And the slope can be defined as the ratio of vertical change (change in y) to the horizontal change (change in x).
Mathematically, we can write
[tex]\text{Slope}=\dfrac{\text{change in y}}{\text{change in x}}=\dfrac{\Delta y}{\Delta x}[/tex]
Now, we have been given that
Roller coaster has a steep drop at a horizontal distance of 25 feet.
Thus, [tex]\Delta x=25\text{ feet}[/tex]
The height of the roller coaster at the bottom of the drop is -150 feet.
Thus, [tex]\Delta y=-150\text{ feet}[/tex]
Using the above- mentioned formula, the average rate of change is given by
[tex]\text{Average rate of change }=\dfrac{-150}{25}[/tex]
On simplifying the fraction
[tex]\text{Average rate of change }=\dfrac{-6}{1}=-6[/tex]
It means for every 1 foot of horizontal distance, the roller coaster moves down by 6 feet.
Please refer the attached graph to understand it better.
Therefore, we can conclude that the average amount that the roller coaster's height changes over each horizontal foot is -6.
Learn more:
Average rate of change: https://brainly.com/question/10961592
Finding Average: https://brainly.com/question/9145375
Keywords:
Average rate of change, slope, change of y over change of x, the ratio of two numbers be the same.
