Question

The intensity I of light from a light bulb varies inversely as the square of the distance d from the light bulb. Suppose I is 360 ​W/m^2 when the distance is 4 m. How much further would it be to a point where the intensity is 250 ​W/m^2​ Simplify

Answer 1

Using this principle, we can solve for the distance where the intensity is a given value. The intensity of light from a light bulb varies inversely as the square of the distance.

Step-by-step explanation:

The intensity of light from a light bulb varies inversely as the square of the distance from the light bulb. In this case, the intensity (I) is given as 360 W/m² when the distance (d) is 4 m. Let's solve for the constant of variation (k) using the given values:

I = k/d²

360 = k/4²

k = 360 * 4²

k = 360 * 16

k = 5760

Now that we have the value of k, we can use it to find the distance (d') where the intensity (I') is 250 W/m²:

I' = 5760/d'²

250 = 5760/d'²

d'² = 5760/250

d'² = 23.04

d' = sqrt(23.04)

d' ≈ 4.8

Therefore, it would be approximately 4.8 meters further to a point where the intensity is 250 W/m².