Algebra work problem

Question

The intensity of a radio signal from the radio station varies inversely as the square of the distance from the station. Suppose the intensity is 8000 units at a distance of 2 miles. What will the intensity be at a distance of 4miles?

Answer 1

 

Hi Tony,

 

As the intensity varies inversely with the square of the distance,

 

it can be formulated as

 

     I = k/d²

 

where I, d, and k represent Intensity, distance, and the proportional constant.

 

If we plug (d, I) = (2, 8000) into the equation above,

 

     8000 = k/2²

 

              = k/4

 

     k = 32000

 

     ∴ I = 32000/d²

 

If we plug d = 4 into the equation,

 

     I = 32000/4²

 

       = 32000/16

 

       = 2000

 

So, the intensity is 2000 units at a distance of 4 miles.