Question

Which of the following exponential regression equations best fits the datashown below?-4-3 -2 -1 0y 0.05 0.20 0.75 2.25 10XOA. y= 10.84.1.77XB. y = 3.14 4.98*OC. y= 8.46.3.51*OD. y = 5.32 2.23*1302100335041250▸

Answer 1

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.

`\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}`

Equation A is incorrect since the values of y do not correspond to the values in the table.

Equation B:

`\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}`

Equation B is incorrect.

Equation C:

`\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}`

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:

`y=8.46*3.51^x`

ANSWER: C

`y=8.46*3.51^x`