Question

Which of the following best models the data in the table?

Type of Function

This table presents the x and y values to identify the function that most accurately models the given dataset.
x y
2
8.5
4
46
6
107.5
8
193
(1 point)
Responses

linear
linear

exponential
exponential

quadratic
quadratic

cubic
cubic
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Answer 1

Quadratic.

Reason: y-values 8.5, 46, 107.5, 193 have first differences 37.5, 61.5, 85.5 and constant second differences 24, so the data fits a quadratic. (The quadratic is y = 3x^2 + 0.75x − 5.)