the average rate of change from x = 0 to x = 15 is about -4.667. how does the average rate of change from x…

Explanation:

Step1: Calculate the average rate of change from (x = 0) to (x=20)

The formula for the average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}). Here, (a = 0), (f(0)=80), (b = 20), (f(20)=10). So, the average rate of change is (\frac{10 - 80}{20-0}=\frac{-70}{20}=-3.5)

Step2: Compare the two average rate of change values

We have two average - rate - of - change values: (-4.667) (from (x = 0) to (x = 15)) and (-3.5) (from (x = 0) to (x = 20)). Since (-3.5> - 4.667) (because when comparing two negative numbers, the number with a smaller magnitude is larger. For example, (-3.5=-\frac{7}{2}) and (-4.667 =-\frac{14}{3}), and (\frac{7}{2}=\frac{21}{6}), (\frac{14}{3}=\frac{28}{6}), (\frac{21}{6}<\frac{28}{6}) so (-\frac{21}{6}>-\frac{28}{6}))

Answer:

The average rate of change from (x = 0) to (x = 20) ((-3.5)) is greater than the average rate of change from (x = 0) to (x = 15) ((-4.667))