Question

Find the average rate of change of f(x) = 3(2)* between x = 1 and x = 4​

Answer 1

Question:

Find the average rate of change of f(x) = 3(2)^x between x = 1 and x = 4

Answer:

The average rate of change is 14

Solution:

The rate of change is given by formula:

$\text { Average Rate }=\frac{f(b)-f(a)}{b-a}$

Here the given interval is x = 1 and x = 4

Therefore, the formula becomes,

$\text { Average Rate }=\frac{f(4)-f(1)}{4-1}\\\\\text { Average Rate }=\frac{f(4)-f(1)}{3}$

Let us find f(4) and f(1)

Given function is:

$f(x)=3(2)^x$

Substitute x = 4 in function

$f(4)=3(2)^4\\\\f(4) = 3 \times 16 = 48$

Thus f(4) = 48

Substitute x = 1 in function

$f(1) = 3(2)^1\\\\f(1) = 6$

Now substitute the values back into formula

$\text { Average Rate }=\frac{f(4)-f(1)}{3}\\\\\text { Average Rate }= \frac{48-6}{3}\\\\\text { Average Rate }= 14$

Thus average rate of change is 14