Question

This table presents the x and y values to identify the function that most accurately models the given dataset.
x
−2
−1
0 1 2 3
y
1.75 3.5 7 14 28 56
Option #1: f(x)=(2⋅7)x


Option #2: f(x)=7⋅2x


Option #3: f(x)=2⋅7x


(1 point)

Answer 1

Option #2.

Reason: y doubles each time x increases by 1 and y(0)=7, so y = 7·2^x. Check: 7·2^0 = 7, 7·2^1 = 14, 7·2^{-1} = 3.5, etc. Options #1 and #3 give wrong values at x=0 (14^0 = 1 and 2·7^0 = 2).