Question

Suppose that the height of the slide is 2 ft when x equals 20. What is the average rate of change over the entire slide?

a) 0.1 ft/ft
b) 0.05 ft/ft
c) 0.15 ft/ft
d) 0.2 ft/ft

Answer 1

The average rate of change for the slide is the change in height divided by the length of the slide. When the height changes by 2 ft over a length of 20 ft, the average rate of change is 0.1 ft/ft.

Step-by-step explanation:

The average rate of change of the slide's height over the entire length of the slide can be determined by the formula for the slope or rate of change, which is ∆height/∆length. The information provided tells us that at x=20 feet (entire length of the slide), the height is 2 feet.

To find the average rate of change (∆height/∆length), we divide the total change in height by the total length of the slide: average rate of change = height change (2 ft) / length change (20 ft) = 2/20 = 0.1 ft/ft.

Therefore, the correct answer to the given options is a) 0.1 ft/ft.