Math CentralQuandaries & Queries


Question from david, a student:

I have this question which I am supposed to set it up and solve as a differential equation. I know how to solve the differential equation but I am having hard time understanding this question. Here is the question: The intensity of light in the ocean decreases the deeper you dive. In fact, the rate at which the intensity decreases is proportional to the current intensity. Setup the corresponding differential equation and solve for I(Y), the intensity I as a function of current intensity Y. If the light intensity 2m below the surface is 25% of the intensity at the surface, what is the intensity 5m below the surface? Can you please explain to me what does it mean by current intensity and how do I set this equation up. Thanks for the help.

Hi David,

The term "current intensity" here refers to the intensity at that depth. Current refers to time not the ocean current. So if the intensity at depth y metres below the surface is I(y) then dI(y)/dy is proportional to I(y).

Does this help?


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