Question

1. is this function linear, quadratic, or exponential?

x	y
2	0.9
3	2.7
4	8.1
5	24.3

Explanation:

Step1: Check linearity (constant Δy)

Calculate differences between consecutive y-values:
$0.9 - 0.3 = 0.6$
$2.7 - 0.9 = 1.8$
$8.1 - 2.7 = 5.4$
$24.3 - 8.1 = 16.2$
Differences are not constant, so not linear.

Step2: Check quadratic (constant Δ(Δy))

Calculate differences of the differences:
$1.8 - 0.6 = 1.2$
$5.4 - 1.8 = 3.6$
$16.2 - 5.4 = 10.8$
Second differences are not constant, so not quadratic.

Step3: Check exponential (constant ratio)

Calculate ratios of consecutive y-values:
$\frac{0.9}{0.3} = 3$
$\frac{2.7}{0.9} = 3$
$\frac{8.1}{2.7} = 3$
$\frac{24.3}{8.1} = 3$
Ratios are constant, so it is exponential.

Answer:

Exponential