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?
ORIGINAL lumens = 1200 l
NEW intensity = 1200 e^(-.12d) lumens
Difference (the amount of change) = 1200 - 1200 e^(-.12d) over a distance 'd '
(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