Question

X values:−10,−3-, 4, 11

y values: 1, 6, 30, 120

Is the relationship linear, exponential, or neither?

Answer 1

the correct answer is Neither.

Answer 2

It is neither linear nor exponential.

Explanation:

x values: −10,−3, 4, 11

y values: 1, 6, 30, 120

Slope = rate of change

`m = (y_2-y_1)/(x_2-x_1)\\m = (6-1)/(-3+10)\\m=(5)/(7)`

`\\m = (y_3-y_2)/(x_3-x_2)\\m = (30-6)/(4+3)\\m=(24)/(7)`

Since rate of change is not constant . So, It is not linear

If the average rate of change is constant, then the function is linear.

If the ratio of consecutive outputs is constant, then the function is exponential.

So,
`(y_2)/(y_1)=(6)/(1)=5\\(y_3)/(y_2)=(30)/(6)=6\\(y_4)/(y_3)=(120)/(30)=4`

Since the ratio of consecutive outputs is not constant.

So, It is not exponential

Hence it is neither linear nor exponential.