Question

The tallest escalator on the London Underground system is at Angel Station. It rises to a height of 90 feet over a horizontal distance of 200 feet. Let e(x) be the height of one of the escalator's steps as a function of the horizontal distance from the bottom step.
The following table shows the coordinates of a linear function.

x ƒ(x)
-5 -1 1/9
-4 -8/9
0 0
2 4/9
3 2/3

Find and compare the rate of change of e(x) and f(x). Which function has the greater rate of change and by how much?

Answer 1

@Lily2913 @DanJS @dan815

Answer 2

e(x) = 90/200 = 0.45
f(x) = 0.222

so the rate of change of the escalator is twice as great as the rate of change of f(x)

Answer 3

the rate of change is the slope, change in vertical value per change in horizontal value