Question

What is the average rate of change between

Answer 1

Rate of change=R∆=(y2-y1)/(x2-x1)=∆y/∆x

(X1,Y1)(X2,Y2)

(1,2)(2,4)

R∆=∆y/∆x

=(4-2)/(2-1)

R∆=2

(2,4)(3,8)

R∆=(8-4)/(3-2)

R∆=4

(3,8)(4,16)

R∆=(16-8)/(4-3)

R∆=8

Answer 2

Answer:  The average rate of change between x = 1 to x = 2 is 2, from x = 2 to x = 3 is 4 and from x = 3 to x = 4 is 8.

Step-by-step explanation:  We are given to find the rate of change from

x = 1 to x = 2,  x = 2 to x = 3  and  x = 3 to x = 4.

We know that

The average rate of change between x = a to x = b for a function f(x) is given by

$A_v=\dfrac{f(b)-f(a)}{b-a}.$

For the given function f(x), we have from the graph that

f(1) = 2,  f(2) = 4,  f(3) = 8  and  f(4) = 16.

So, the average rate of change from x = 1 to x = 2 is given by

$A_{v1}=\dfrac{f(2)-f(1)}{2-1}=\dfrac{4-2}{1}=2.$

The average rate of change from x = 2 to x = 3 is given by

$A_{v2}=\dfrac{f(3)-f(2)}{3-2}=\dfrac{8-4}{1}=4.$

The average rate of change from x = 3 to x = 4 is given by

$A_{v3}=\dfrac{f(4)-f(3)}{4-3}=\dfrac{16-8}{1}=8.$

Thus, the average rate of change between x = 1 to x = 2 is 2, from x = 2 to x = 3 is 4 and from x = 3 to x = 4 is 8.