SOLUTION: The intensity I of a television signal varies inversely as the square of distance d from the transmitter. If the intensity is 25W/m^2 at a distance of 2 km, how far from the trans

Algebra ->  Coordinate Systems and Linear Equations  -> Linear Equations and Systems Word Problems -> SOLUTION: The intensity I of a television signal varies inversely as the square of distance d from the transmitter. If the intensity is 25W/m^2 at a distance of 2 km, how far from the trans      Log On


   

Question 375493: The intensity I of a television signal varies inversely as the square of distance d from the transmitter. If the intensity is 25W/m^2 at a distance of 2 km, how far from the transmitter are you when the intensity is 2.6W/m^2?
Unfortunately, we did not go over this in class so I've been struggling with trying to figure it out. I want to think the formula to start with is I = k/d^2 after that I am stumped. I don't understand what 2.6W/m^2 represents.
Any help would greatly be appreciated.
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You are off to a good start! You have written the inverse variation function for intensity (I):
I+=+k%2Fd%5E2 Now you need to find the value of k, the constant of variation. You do this by substituting the given values of I+=+25W/m^2 and d+=+2meters:
25+=+k%2F2%5E2 so that...
k+=+100 Now the function for intensity looks like:
I+=+100%2Fd%5E2 Now you can answer the question posed in the problem:
"How far (d) are you from the transmitter when the intensity (I) is 2.6W/m%5E2?
Substitute the values into the last equation:
2.6+=+100%2Fd%5E2 Solve for d%5E2.
d%5E2+=+100%2F2.6 Take the square root of both sides.
d+=+10%2Fsqrt%282.6%29meters.
d+=+6.2meters.
Intensity is Watts per square meter or W%2Fm%5E2