Question

Calculate the average rate of change for the graphed sequence from n = 1 to n = 3. (2 points) graphed sequence showing point 1, 2, point 2, 4, point 3, 8, point 4, 16, point 5, 32, and point 6, 64

Answer 1

the rate of change is y times 2 or (X,Y*2)

Answer 2

The average rate of change is 3.

Explanation:

The given points are

`(1, 2)\\(2,4)\\(3,8)\\(4,16)\\(5,32)\\(6,64)`

Notice that the relation between coordinates is exponential, because y-values are the result of a power with base 2, and x-values represents exponents.

The function that defines this sequence is

`f(x)=2^(x)`

Where the factor that creates this geometric sequence is 2.

However, when we talk about the average rate of change, it's defined as

`r=(\Delta y)/(\Delta x)`

In words, it's the quotient between the change of vertical values and the change of horizontal values.

In this case, we have

`r=(8-2)/(3-1)=(6)/(2)=3`

Therefore, the average rate of change from n = 1 to n = 3 is 3.