Question

the average rate of change from x = 0 to x = 15 is about - 4.667. how does the average rate of change from x = 0 to x = 20 compare to this number? the average rate of change from x = 0 to x = 20 is decreasing faster than slower than the same amount as the average rate of change from x = 0 to x = 15. of the slide is 2 feet, when x = 20. what is the average rate of change over the entire slide?

Explanation:

Step1: Recall average - rate - of - change formula

The average rate of change of a function $y = f(x)$ from $x = a$ to $x = b$ is $\frac{f(b)-f(a)}{b - a}$.

Step2: Analyze the graph

From $x = 0$ to $x = 15$, the average rate of change is about $- 4.667$. From $x=0$ to $x = 20$, the function values change from $y(0)=80$ to $y(20) = 2$. The average rate of change from $x = 0$ to $x = 20$ is $\frac{2 - 80}{20-0}=\frac{-78}{20}=-3.9$.

Step3: Compare the rates

Since $|-3.9|\lt|-4.667|$, the average rate of change from $x = 0$ to $x = 20$ is slower than the average rate of change from $x = 0$ to $x = 15$.

Answer:

slower than