Question

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

Answer 1

-3.98 (nearest hundredth)

Explanation:

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

`(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)= (1)/(16)`

Substituting the values into the equation:

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