find the average rate of change of ( k(x)=\frac{-20}{x - 4} ) over the interval ( 0,3 ).\nwrite your answer…

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

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

Answer

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)