I dont know how to do this Inverse variation

Question

the intensity I of light varies inversely as the square of the distance d from the light source. If the distance from the light source is doubled (see the figure)., determine what happens to the intensity of light at the new location

 

book to lamp 12 

book to lamp 24

 

I=k/d^2

 

What is the setup???

Answer 1

I = k/d²

 

Doubling the distance to the light source:

 

I = k/(2d)²  = k/(4d²) = (1/4)*(k/d²)

 

By doubling the distance to the light source the intensity of light will decrease to 1/4 of the intensity at the original distance. In other word the intensity would be 25% of the original,  that translate to a decrease of 75% 

 

Edit: It can also be approached as follows:

 

I₁ = k/d²

I₂ = k/(2d)²

I₂ = k/(4d²)

I₂ = (1/4)*(k/d²)

I₂ = (1/4)*I₁

 

I hope this helps.