Answer :
Given the table of values:
x -4 -3 -2 -1 0 1 2 3 4
y 0.05 0.20 0.75 2.25 10 30 100 350 1250
Let's find the exponential regression equation that bet fits the data.
To determine the exponential regression equation which fits the data. let's take 3 points from the table:
(x, y) ==> (-4, 0.05), (-1, 2.25 (2, 100)
Plug in the value of the x-coordinate and solve for the value of y in each equation.
We have the following:
Equation A.
[tex]\begin{gathered} At\text{ x = -4:} \\ y=10.84*1.77^{-4}=1.104 \\ \\ At\text{ x = -1:} \\ y=10.84*1.77^{-1}=6.12 \\ \\ At\text{ x = 2:} \\ y=10.84*1.77^2=33.96 \end{gathered}[/tex]Equation A is incorrect since the values of y do not correspond to the values in the table.
Equation B:
[tex]\begin{gathered} At\text{ x = -4:} \\ y=3.14*4.98^{-4}=0.005 \\ \\ At\text{ x = -1:} \\ y=3.14*4.98^{-1}=0.63 \\ \\ At\text{ x = 2:} \\ y=3,14*4.98^2=77.87 \end{gathered}[/tex]Equation B is incorrect.
Equation C:
[tex]\begin{gathered} At\text{ x=-4:} \\ y=8.46*3.51^{-4}=0.055 \\ \\ At\text{ x = -1:} \\ y=8.46*3.51^{-1}=2.41 \\ \\ At\text{ x = 2:} \\ y=8.46*3.51^2=104.22 \end{gathered}[/tex]We can see the values of y here are almost equivalent to the corresponding y-values in the table.
Therefore, the exponential regression equation which best fits the data shown is:
[tex]y=8.46*3.51^x[/tex]ANSWER: C
[tex]y=8.46*3.51^x[/tex]