Question

the average rate of change from ( x = 0 ) to ( x = 16 ) 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 slower than the average rate of change from ( x = 0 ) to ( x = 16 ).
suppose that the height of the slide is 2 feet when ( x = 20 ). what is the average rate of change over the entire slide?

Explanation:

Step1: Recall the formula for average rate of change

The formula for average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\), \(f(0)=100\) (from the graph, when \(x = 0\), \(y=100\)), and \(b = 20\), \(f(20)=2\).

Step2: Calculate the average rate of change

Substitute the values into the formula: \(\frac{2 - 100}{20-0}=\frac{- 98}{20}=-4.9\)

Answer:

\(-4.9\)