The intensity of a radio signal from a radio station varies inversely as the square of the distance from the station. If the intensity is 8000 units at a distance of 2 miles, what will it be at a distance of 13 miles?
A) 189 units
B) 172 units
C) 215 units
D) 153 units

Question

Quizplus · Accepted Answer

The intensity $I$ of a radio signal varies inversely as the square of the distance $d$ from the station, which can be represented by the formula $I = \frac{k}{d^2}$, where $k$ is a constant. Given $I = 8000$ units at $d = 2$ miles, we can find $k = 8000 \times 2^2 = 32000$. At a distance of 13 miles, the intensity $I = \frac{32000}{13^2} = \frac{32000}{169} \approx 189$ units.

The Intensity of a Radio Signal from a Radio Station