Question

find the average rate of change of ( k(x)=\frac{-20}{x - 4} ) over the interval ( 0,3 ).
write your answer as an integer, fraction, or decimal rounded to the nearest tenth.
simplify any fractions.

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, \(a = 0\), \(b=3\), and \(k(x)=\frac{-20}{x - 4}\).

Step2: Calculate \(k(3)\) and \(k(0)\)

• For \(x = 3\): \(k(3)=\frac{-20}{3 - 4}=\frac{-20}{-1}=20\).
• For \(x = 0\): \(k(0)=\frac{-20}{0 - 4}=\frac{-20}{-4}=5\).

Step3: Apply the average - rate - of - change formula

\(\frac{k(3)-k(0)}{3 - 0}=\frac{20 - 5}{3}=\frac{15}{3}\).

Answer:

\(5\)