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# The intensity, Io, of a light source is reduced to I after passing through d meters of fog according to the formula I = Ioe−0.12d. If 1,200 lumens of light

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The intensity, Io, of a light source is reduced to I after passing through d meters of fog according to the formula I = Ioe−0.12d. If 1,200 lumens of light are present initially, what is an equivalent expression written as a percentage rate of lumens lost?

Guest Feb 14, 2017
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ORIGINAL lumens = 1200 l

NEW intensity  = 1200 e^(-.12d) lumens

Difference  (the amount of change)  =  1200 - 1200 e^(-.12d)     over a distance 'd '

Percentage change

(1200-1200 e^(-.12d) )/1200    x 100

Percentage  RATE of change (average over distance d) would be this divided by d

percentage rate of change    (1200-1200e^(-.12d)) / (1200 d) x 100  =  (1 - e^(-.12d))/d    x 100

ElectricPavlov  Feb 14, 2017
edited by ElectricPavlov  Feb 14, 2017

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