Question

Which function best models the dataset in the table?

This table presents the x and y values to identify the function that most accurately models the given dataset.
x
−5
−2
−1
0 1 2 5 8 12
y
6.2 8.3 9.1 10 11 12.1 16.1 21.4 31.4
Option #1: f(x)=1.467x+10.696


Option #2: f(x)=10.004(1.100)x


Option #3: f(x)=0.066x2+0.981x+9.810


(1 point)
Option #
is the correct response.

Answer 1

Option #2.

Reason: f(x)=10.004(1.100)^x produces predictions that match the table values almost exactly (e.g. f(-5)≈6.21, f(0)=10.004, f(5)≈16.11, f(12)≈31.40), giving much smaller residuals than the linear or quadratic options.