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 slower than the average rate of change from ( x = 0 ) to ( x = 15 ). complete suppose that the height of the slide is 2 feet, when ( x = 20 ). what is the average rate of change over the entire slide? done

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 \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 0\), \(b=20\), \(f(0)=80\) and \(f(20) = 2\).

Step2: Substitute the values into the formula

Substitute \(a = 0\), \(b = 20\), \(f(0)=80\) and \(f(20)=2\) into \(\frac{f(b)-f(a)}{b - a}\). We get \(\frac{2 - 80}{20-0}\).

Step3: Simplify the expression

First, calculate the numerator \(2-80=-78\). Then, divide by the denominator \(20\). So, \(\frac{-78}{20}=-3.9\)

Answer:

\(-3.9\)