Question

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

Explanation:

Step1: Calculate first differences (Δy)

$\Delta y_1 = -473.85 - (-585) = 111.15$
$\Delta y_2 = -374.4 - (-473.85) = 99.45$
$\Delta y_3 = -286.65 - (-374.4) = 87.75$
$\Delta y_4 = -210.6 - (-286.65) = 76.05$

Step2: Calculate second differences (Δ²y)

$\Delta^2 y_1 = 99.45 - 111.15 = -11.7$
$\Delta^2 y_2 = 87.75 - 99.45 = -11.7$
$\Delta^2 y_3 = 76.05 - 87.75 = -11.7$

Step3: Classify the function

Since second differences are constant, the function is quadratic.

Answer:

quadratic