Question

As light from the surface penetrates water, its intensity is diminished. In the clear waters of the Caribbean, the intensity is decreased by 15 percent for every 3 meters of depth. Thus, the intensity will have the form of a general exponential function.
(a) If the intensity of light at the water’s surface is I◦, find a formula for l(d), the intensity of light at a depth of d meters. Your formula should depend on on I◦ and d

Answer 1

The answer is I(d) = I◦(0.94727)^d

Answer 2

are you asking how they derived that equation?

if so, let's start off with a basic exponential equation

I(d) = I◦ (1-0.15)^(d/3)

this represents a decrease of 15% every time d reaches a multiple of 3

apply the exponent rule a^(mn) = (a^m)^n to get

I(d) = I◦ [(1-0.15)^(1/3)]^d

when you simplify that big expression inside the square brackets, you get 0.94727 as the original answer key states

Answer 3

let me know if I'm off base with what you're looking for

Answer 4

no, I got it thanks