algebra 2 question in description

Question

The intensity of a radio signal varies inversely as the square of the distance from the transmitter. If a person stands 3km away from a transmitter and measures an intensity of 20 watts per square meter (W/m²), approximately how far must a person staying to measure an intensity of 3.7 W/m²

 

A.1km

B.3km

C.4km

D.7km

Answer 1

Set a proportional relationship between intensity and square of distance.

 

Let I = intensity

Let r = distance

 

I ∝ 1/r²

 

 

We can established an equation.

 

I = K/r² ,  K is constant

 

We need to solve for K using the initial values.

 

 

K = r²I

 

r = 3 km

I = 20 W/m²

 

Since we have different units m and km.  Let's convert km to m.

 

1 km = 1000 m

3 km = 3000 m

 

 

K = (3000 m)² * (20 W/m²)

K = (9000000 m²) * (20 W/m²)

K = 180000000 W

 

 

Next, we find the distance using our K value and 3.7 W/m².

 

r² = (K / I)

r² = (180000000 W) / (3.7 W/m²)

r² = 48648648.65 m²

 

Square-root both sides of equation to find r.

 

r = 6974.76 m

 

 

Since the answer is km, divide this value by 1000.

 

6974.76 / 1000 = 6.97476

 

 

Your answer is (D).