Respuesta :

mhanifa

Answer:

  • b) -6

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Find the value of the function at the endpoints of the given interval

  • x = - 2 ⇒ y = 4(1/2)⁻² = 4(2)² = 4(4) = 16
  • x = 0  ⇒ y = 4(1/2)⁰ = 4(1) = 4

Average rate of change is

  • Change in y / change in x =
  • (4 - 16)/(0 - (-2)) =
  • - 12 / 2 =
  • - 6

Correct choice is B.

semsee45

Answer:

b)  -6

Step-by-step explanation:

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

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

Given the interval is [-2, 0]:

  • a = -2
  • b = 0

Substitute the endpoints of the interval into the function and solve:

[tex]\begin{aligned}x=-2 \implies f(-2)&=4\left(\dfrac{1}{2}\right)^{-2}\\& = 4(4)\\&=16\end{aligned}[/tex]

[tex]\begin{aligned}x=0 \implies f(0)&=4\left(\dfrac{1}{2}\right)^{0}\\& = 4(1)\\&=4\end{aligned}[/tex]

Therefore:

[tex]\begin{aligned}\implies\dfrac{f(b)-f(a)}{b-a}&=\dfrac{f(0)-f(-2)}{0-(-2)}\\\\&=\dfrac{4-16}{0+2}\\\\&=\dfrac{-12}{2}\\\\&=-6\end{aligned}[/tex]

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