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Given the function defined in the table below, find the average rate of change, in
simplest form, of the function over the interval 16 ≤ x ≤ 40.

Given the function defined in the table below find the average rate of change in simplest form of the function over the interval 16 x 40 class=

Respuesta :

semsee45

Answer:

[tex]\dfrac{1}{4}[/tex]

Step-by-step explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by the formula:

[tex]\boxed{\dfrac{f(b)-f(a)}{b-a}}[/tex]

Given interval:

16 ≤ x ≤ 40

Therefore:

  • a = 16
  • b = 40

From inspection of the given table:

  • f(a) = f(16) = 10
  • f(b) = f(40) = 16

Substitute the found values into the formula:

[tex]\begin{aligned}\implies \dfrac{f(b)-f(a)}{b-a} & = \dfrac{f(40)-f(16)}{40-16}\\\\ & =\dfrac{16-10}{40-16}\\\\& = \dfrac{6}{24}\\\\& = \dfrac{1}{4}\end{aligned}[/tex]

Therefore, the average rate of change over the given interval is ¹/₄.

Learn more about rates of change here:

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