Question

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

linear
quadratic
exponential

Explanation:

Step1: Calculate first differences (Δy)

$\Delta y_1 = 151 - 96.64 = 54.36$
$\Delta y_2 = 217.44 - 151 = 66.44$
$\Delta y_3 = 295.96 - 217.44 = 78.52$
$\Delta y_4 = 386.56 - 295.96 = 90.60$

Step2: Calculate second differences (Δ²y)

$\Delta^2 y_1 = 66.44 - 54.36 = 12.08$
$\Delta^2 y_2 = 78.52 - 66.44 = 12.08$
$\Delta^2 y_3 = 90.60 - 78.52 = 12.08$

Step3: Classify the function

Constant second differences mean the function is quadratic.

Answer:

quadratic