Question

x 0 1 2 3
y 1 3 9 27
is the relationship linear, exponential, or neither?
choose 1 answer:
a linear
b exponential
c neither

Explanation:

Step1: Check linearity (constant slope)

Slope between $(0,1)$ & $(1,3)$: $\frac{3-1}{1-0}=2$
Slope between $(1,3)$ & $(2,9)$: $\frac{9-3}{2-1}=6$
Slopes are not equal, so not linear.

Step2: Check exponential (constant ratio)

Ratio between $y$-values: $\frac{3}{1}=3$, $\frac{9}{3}=3$, $\frac{27}{9}=3$
Constant ratio of 3, so exponential.

Answer:

B. Exponential