Question

Find the average rate of change​

Answer 1

`(26)/(3)`

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 function:
`f(x)=3^(x-1)+2`

Given interval: 1 ≤ x ≤ 4

Therefore, a = 1 and b = 4

Therefore, find the value of the given function when x = 1 and x = 4:

`\begin{aligned}\implies f(1) & =3^(1-1)+2\\ & = 3^0+2\\ & = 1+2\\ & = 3 \end{aligned}`

`\begin{aligned} \implies f(4) & = 3^(4-1)+2 \\ & = 3^3+2\\ & = 27+2\\ & = 29 \end{aligned}`

Substitute the found values into the formula:

`\begin{aligned}\implies (f(b)-f(a))/(b-a) & =(f(4)-f(1))/(4-1)\\\\ & =(29-3)/(4-1)\\\\ & = (26)/(3) \end{aligned}`