Question

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 the average rate of change of a function \(y = f(x)\) over the interval \([a,b]\) is \(\frac{f(b)-f(a)}{b - a}\). For a slide, assume the starting point is \((0, h_1)\) and the ending point is \((x_2,y_2)\). Here, assume the starting height \(h_1\) (when \(x = 0\)) is \(0\) (ground - level start in a typical slide context) and \(x_2=20\), \(y_2 = 2\).

Step2: Substitute values into the formula

Using the formula \(\text{Average Rate of Change}=\frac{y_2 - y_1}{x_2 - x_1}\), substitute \(y_1 = 0\), \(x_1=0\), \(y_2 = 2\), \(x_2 = 20\). Then \(\text{Average Rate of Change}=\frac{2-0}{20 - 0}\).

Step3: Simplify the expression

\(\frac{2}{20}=\frac{1}{10}=0.1\)

Answer:

\(0.1\)