You have the function f(x) = 0.5^x
In the table, y is basically f(x). They really should have written f(x) to be consistent.
To get the first box in the y column, plug the given x-value -3 into the equation as x.
Given equation: y = 0.5^x
y = 0.5^-3
[tex]y= \frac{1}{0.5^3} = 8[/tex]