Question

x 2 9 16 23
y 4 8 16 32
is the relationship linear, exponential, or neither?
choose 1 answer:
a linear
b exponential
c neither

Explanation:

Step1: Check linearity (constant Δy/Δx)

First, calculate differences in $x$:
$\Delta x_1 = 9-2=7$, $\Delta x_2=16-9=7$, $\Delta x_3=23-16=7$ (constant)
Calculate differences in $y$:
$\Delta y_1=8-4=4$, $\Delta y_2=16-8=8$, $\Delta y_3=32-16=16$ (not constant)
Slopes: $\frac{4}{7}$, $\frac{8}{7}$, $\frac{16}{7}$ (not equal)

Step2: Check exponentiality (constant ratio)

Calculate ratios of consecutive $y$-values:
$\frac{8}{4}=2$, $\frac{16}{8}=2$, $\frac{32}{16}=2$ (constant ratio), and $x$ increases by a constant interval.

Answer:

B. Exponential