Many Physical Quantities Are Connected by Inverse Square Laws, That $f(x)=k x^{-2}$

question 9

Multiple Choice

Many physical quantities are connected by inverse square laws, that is, by power functions of the form $f(x) =k x^{-2}$ . In particular, the illumination of an object by a light source is inversely proportional to the square of the distance from the source. Suppose that after dark you are in a room with just one lamp and you are trying to read a book. The light is too dim and so you move $\frac{1}{3} \text { th }$ the distance to the lamp. How much brighter is the light?

• A) \(\frac{4}{9}\) times
• B) \(\frac{9}{2}\) times
• C) 9 times.
• D) \(\frac{3}{2}\) times
• E) 9 times