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 the average rate of change from x = 0 to x = 15.

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 $\frac{f(b)-f(a)}{b - a}$. From the graph, when $x = 0$, $y=80$; when $x = 15$, assume $y = y_1$ and the average rate of change from $x = 0$ to $x = 15$ is $\frac{y_1 - 80}{15-0}\approx - 4.667$. When $x = 20$, assume $y = y_2$. The average rate of change from $x = 0$ to $x = 20$ is $\frac{y_2 - 80}{20 - 0}$.

Step2: Analyze the graph

The graph is a decreasing curve. As we move from $x = 15$ to $x = 20$, the function values continue to decrease. The secant - line from $(0,80)$ to $(20,y_2)$ is steeper (more negative) than the secant - line from $(0,80)$ to $(15,y_1)$.

Answer:

more negative than