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 the formula for average rate of change

The formula for 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: Find the average rate of change from \(x = 0\) to \(x=20\)

From the graph, when \(x = 0\), \(y=80\) (since the \(y\) - intercept is \(80\)), and when \(x = 20\), \(y = 0\).
Using the formula \(\frac{f(20)-f(0)}{20 - 0}=\frac{0 - 80}{20-0}=\frac{- 80}{20}=-4\)

Step3: Compare the two average rate of changes

The average rate of change from \(x = 0\) to \(x = 15\) is \(\frac{f(15)-f(0)}{15 - 0}\). From the graph, when \(x = 15\), \(y = 20\), so \(\frac{20 - 80}{15-0}=\frac{-60}{15}=-4.667\) (approx).
Since \(-4>-4.667\), the average rate of change from \(x = 0\) to \(x = 20\) is greater than the average rate of change from \(x = 0\) to \(x = 15\)

Answer:

greater than