Question

The table of values represents an exponential function f(x).

Answer 1

Answer:

-3.98 (nearest hundredth)

Step-by-step explanation:

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

$\dfrac{f(b)-f(a)}{b-a}$

Given interval:  -2 ≤ x ≤ 2

$\implies a = -2$

$\implies b = 2$

$\implies f(a) = f(-2)=16$

$\implies f(b) =f(2)= \dfrac{1}{16}$

Substituting the values into the equation:

$\begin{aligned}\implies \textsf{rate of change} & =\dfrac{\frac{1}{16}-16}{2-(-2)}\\\\ & = \dfrac{-\frac{255}{16}}{4}\\\\ & = -\dfrac{255}{64}\\\\ & = -3.98\: \sf (nearest\:hundredth)\end{aligned}$