## Intermediate Algebra (6th Edition)

reduces by $\dfrac{1}{4} \text{ times}$
The variation model described by the problem is $I=\dfrac{k}{d^2} ,$ where $I$ is the intensity of light and $d$ is the distance from the light source. Substituting $d=12$ in the equation above results to \begin{array}{l}\require{cancel} I=\dfrac{k}{12^2} \\\\ I=\dfrac{k}{144} .\end{array} Substituting $d=24$ in the equation above results to \begin{array}{l}\require{cancel} I=\dfrac{k}{24^2} \\\\ I=\dfrac{k}{576} .\end{array} Hence, when $d=24$ (doubled), the intensity of the light reduces by $\dfrac{1}{4} \text{ times} .$