Which equation describes the relationship between the variables in the table below?

Answer:
D) y = 9^x, each y value is the previous y-value multiplied by another 9.
Step-by-step explanation:
We are given table values.
When x = -1 , y = 0.111
When x =1, y = 9
When x =2, y = 81
Now let's check with this with the each function.
y = x^9
When x = -1, y = (-1)^9 = -1
So this is not right function.
y = 9x^2 is also not the right function for the given table values.
y = 9(-1)^2 = 9(1) = 9
y = 9x is not also the right function.
[tex]y = 9^x[/tex] is the correct function for the given table values.
Let's check with a couple of points.
When x = -1, y = 9^-1, this can be written as 1/9 = 0.1111
When x = 2, y = 9^2 = 9*9 = 81
When x = 4, y = 9^4 = 9*9*9*9 = 6,561
Therefore, the answer is D) y = 9^x, each y value is the previous y-value multiplied by another 9.