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Question

The intensity of light​ (in foot-candles) varies inversely as the square of​ x, the distance in feet from the light source. The intensity of light 2 feet from the source is 12 ​foot-candles. How far away is the source if the intensity of light is

3 ​foot-candles?

Answer 1

So we have our equation, intensity = k/distance^2.

If we know that the 2 feet from the source is 12 foot-candles, we have the equation

12=k/2^2

12=k/4

k=48

But we need to find the the distance when our intensity is 3, which we can do now that we have found k.

So we set up the new equation,

3=48/d^2

3(d^2)=48

d^2=16

d=4

And we have our answer that it is 4 feet away.