Question

light intensity ($i$) is proportional ($propto$) to the inverse square of distance ($d$) of a subject from a light source. the relationship in intensities for subjects at different distances from the same source can be likewise seen as a ratio or proportional relationship.
$i propto \frac{1}{d^{2}}$
a proportional relationship can be mathematically expressed as follows for light intensity ($i$) in lumens when a subject is at the light source.
$\frac{lumens at current distance}{lumens at origin or source}=\frac{1}{d^{2}}$
so, if a light intensity ($i$) is 21 lumens at 3 distance from the source, what is the light intensity ($i$) at the origin or source?
round the value to the nearest tenth if necessary. you do not need to include a label for lumens. only the number, rounded to the tenth, will be necessary.

Explanation:

Step1: Substitute the given values into the formula

Let \(I_{current} = 21\), \(d = 3\). The formula is \(\frac{I_{current}}{I_{source}}=\frac{1}{d^{2}}\). Substituting gives \(\frac{21}{I_{source}}=\frac{1}{3^{2}}\).

Step2: Solve for \(I_{source}\)

Cross - multiply: \(I_{source}\times1=21\times3^{2}\). Since \(3^{2}=9\), then \(I_{source}=21\times9\).

Step3: Calculate the value

\(21\times9 = 189\).

Answer:

189