Write an equation that expresses the relationship. Use k as the constant of variation.
-The intensity I of light varies inversely as the square of the distance D from the source. If the intensity of illumination on a screen 36 ft from a light is 3.9 foot-candles, find the intensity on a screen 90 ft from the light.
A) 0.624 foot-candles
B) 1.56 foot-candles
C) 9.75 foot-candles
D) 24.38 foot-candles

Question

Quizplus · Accepted Answer

The intensity $I$ of light varies inversely as the square of the distance $D$ from the source, which can be expressed as $I = \frac{k}{D^2}$. Given $I = 3.9$ foot-candles at $D = 36$ ft, we find $k = 3.9 \times 36^2$. To find the intensity at $D = 90$ ft, we use $I = \frac{k}{90^2}$, resulting in $I = 0.624$ foot-candles.

Write an Equation That Expresses the Relationship