Find an equation of variation for the given situation....

Find an equation of variation for the given situation. Intensity of Light. The intensity $I$ of light from a light bulb varies inversely as the square of the distance $d$ from the bulb. Suppose that $I$ is $90 \mathrm{W} / \mathrm{m}^{2}$ (watts per square meter) when the distance is $5 \mathrm{m}$. How much farther would it be to a point where the intensity is $40 \mathrm{W} / \mathrm{m}^{2} ?$

Find an equation of variation for the given situation.
Intensity of Light. The intensity $I$ of light from a light bulb varies inversely as the square of the distance $d$ from the bulb. Suppose that $I$ is $90 \mathrm{W} / \mathrm{m}^{2}$ (watts per square meter) when the distance is $5 \mathrm{m}$. How much farther would it be to a point where the intensity is $40 \mathrm{W} / \mathrm{m}^{2} ?$

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Key Concepts

Inverse Variation

This is a type of relationship between two variables where one variable increases while the other decreases so that their product remains constant. In problems involving intensity and distance, the inverse variation implies that as the distance increases, the intensity decreases proportionally according to a constant multiplier.

Inverse Square Law

A specific form of inverse variation, the inverse square law states that a quantity is inversely proportional to the square of the distance from a source. This concept is fundamental in understanding physical phenomena such as light and gravitational intensity, where doubling the distance results in the intensity falling to one-fourth of its original value.

Proportionality Constant

In any variation relation, the proportionality constant is the fixed value that relates the two variables. It is determined by plugging in known values from the relationship and is essential for formulating the exact mathematical equation that describes the variation.

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