Question

X 0 1 2 3

y 1 3 9 27
Is the relationship linear, exponential, or neither?
Choose 1 answer:


(Choice A)
A
Linear

(Choice B)
B
Exponential

(Choice C)
C
Neither

Answer 1

Exponential

Explanation:

Answer 2

Explanation:

Let's check for linear first. We will do that by usingseveral of the points in the slope formula and seeing if the slope between the points is the same each time. Using (0, 1) and (1, 3):

`m=(3-1)/(1-0)=2` then using the next 2 sets of coordinates (1, 3) and (2, 9):

`m=(9-3)/(2-1)=6`

So obviously this is not linear since the slope values are different. Let's try exponential first. We will use the first 2 coordinates to write the model and then test it out on another point. Use (0, 1) and (1, 3) in

`y=a(b)^x` so

`1=a(b)^0` and

a = 1. Using that a value along with the next coordinate we will write a model:

`3=1(b)^1` so

b = 3. The model then is

`y=1(3)^x`

Let's test it out. Sub in a 2 for x and see if we do in fact that y = 9:

`y=1(3)^2` and

y = 9

This is exponential. You can try the next coordinate if you'd like, but since 3 cubed = 27, you know it works. Choice B Exponential