Question

the intensity of light at a distance is modeled by, $i = sqrt4{\frac{p}{d}}$ where $p$ is the power of the source and $d$ is the distance. if $p = 10,000$ and $d = 10$, what is $i$, the intensity?
4000
250
32
6

Explanation:

Step1: Substitute values into formula

Substitute $P = 10000$ and $d = 10$ into $I=\sqrt[4]{\frac{P}{d}}$, we get $I=\sqrt[4]{\frac{10000}{10}}$.

Step2: Simplify the fraction inside the root

$\frac{10000}{10}=1000$, so $I = \sqrt[4]{1000}$.

Step3: Calculate the fourth - root

We know that $32^2=1024$, $250^2 = 62500$, $4000^2=16000000$, $6^2 = 36$. And $\sqrt[4]{1000}\approx 5.62$. Among the given options, the closest value to $\sqrt[4]{1000}$ is 6.

Answer:

6