Question

is this function linear, quadratic, or exponential?

x | y
-4 | 0.04
-3 | 0.12
-2 | 0.36
-1 | 1.08
0 | 3.24

options:
linear
quadratic
exponential

Explanation:

Step1: Check first differences (linear)

Calculate $\Delta y = y_{n+1}-y_n$:
$0.12-0.04=0.08$, $0.36-0.12=0.24$, $1.08-0.36=0.72$, $3.24-1.08=2.16$
Differences are not constant.

Step2: Check second differences (quadratic)

Calculate $\Delta^2 y = (\Delta y)_{n+1}-(\Delta y)_n$:
$0.24-0.08=0.16$, $0.72-0.24=0.48$, $2.16-0.72=1.44$
Second differences are not constant.

Step3: Check ratios (exponential)

Calculate $\frac{y_{n+1}}{y_n}$:
$\frac{0.12}{0.04}=3$, $\frac{0.36}{0.12}=3$, $\frac{1.08}{0.36}=3$, $\frac{3.24}{1.08}=3$
Ratios are constant.

Answer:

exponential