The intensity of a light varies inversely as the square of the distance from the light source. If the intensity from a light source 3 feet away is 8 lumens, what is the intensity at a distance of 2 feet?

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Answer 1 · 2016-04-25T19:58:26

Light intensity at 2 feet is 8 lumens

Let intensity be #i#

Let the distance from light source be #d#
Let the constant of association be #k#

Then: #i=k/d^2#

'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Given condition#-> i=8" at "d=3#

#=> 8=k/(3^2)#

Multiply both sides by #3^2#

#=> 8xx3^2=k/(cancel(3^2)) xxcancel(3^2) = 72#

Then: #i=72/d^2#
'~~~~~~~~~~~~~~~~~~~~~~~~~

So at 2 feet we have: #i=72/2^2 =18#