Inverse variation:
[tex]y=\frac{k}{x^2}[/tex]
y - the intensity of illumination, x - the distance from the light source
When the distance is 8 inches, the intensity is 12 lm.
[tex]12=\frac{k}{8^2} \\
12=\frac{k}{64} \\
12 \times 64=k \\
k=768 \\ \Downarrow \\
y=\frac{768}{x^2}[/tex]
When the distance is x inches, the intensity is 3 lm.
[tex]3=\frac{768}{x^2} \\
3x^2=768 \\
x^2=\frac{768}{3} \\
x^2=256 \\
x=-16 \hbox{ or } x=16[/tex]
The distance can't be a negative number, so x=16.
The photoelectric cell is 16 inches from the light source.
