Given equation:
[tex]$f(x)=-8\left(\frac{5}{2}\right)^{x}[/tex]
Let y = f(x)
To complete the given table let us find the value of y.
Find the value of y for the corresponding x given.
Substitute x = –3 in f(x).
[tex]$f(x)=-8\left(\frac{5}{2}\right)^{-3}[/tex]
[tex]$=-8\left(\frac{8}{125}\right)[/tex]
[tex]$f(x)=\frac{-64}{125}[/tex]
Substitute x = –1 in f(x).
[tex]$f(x)=-8\left(\frac{5}{2}\right)^{-1}[/tex]
[tex]$=-8\left(\frac{2}{5}\right)[/tex]
[tex]$f(x)=\frac{-16}{5}[/tex]
Substitute x = 0 in f(x).
[tex]$f(x)=-8\left(\frac{5}{2}\right)^{0}[/tex]
[tex]$=-8(1)[/tex]
[tex]$f(x)=-8[/tex]
Substitute x = 2 in f(x).
[tex]$f(x)=-8\left(\frac{5}{2}\right)^{2}[/tex]
[tex]$=-8\left(\frac{25}{4}\right)[/tex]
[tex]$f(x)=-50[/tex]
Now, substitute the values in the given table.
The image of the table is given below.
