```Question 117509
I suspect that the tutors on this site are ignoring this problem because it lacks some detail.
I can't answer your problem either, but I'll give you some thoughts that might help to
get you started.
.
I'm going to assume that x represents the depth in cm.
.
I have no concrete feel for what you mean by the term "Photic Zone" so I'm not sure how
to provide you with an estimate. For example, is the Photic Zone that depth where the light
is down to 90% of the surface light ... or what is it.
.
The equation you gave is:
.
{{{I = I[o]C^x}}}
.
I interpret this to mean that I is the light at a given depth. You did say that {{{I[o]}}} is the
"amount" of light at the surface. I'm not sure what C is, other than it is a fraction
or decimal that has a value less than 1 but greater than zero.
.
If my assumption and interpretations are correct we might get a meaningful value for C through
the following method.
.
You know that at a depth of 10 cm (x = 10) the light is 50% (or 0.5 times) the amount at the surface. Since
the amount at the surface is {{{I[o]}}} then you can substitute {{{0.5*I[o]}}} for I and the
equation becomes:
.
{{{0.5*I[o] = I[o]*C^10}}}
.
Since {{{I[o]}}} is a factor of both sides, you can divide both sides by {{{I[o]}}} and the
{{{I[o]}}} terms drop out, reducing the equation to:
.
{{{0.5 = C^10}}}
.
You can now solve for C by taking the 10th root of both sides. You can do this on an ordinary
scientific calculator by raising both sides to the {{{1/10}}} power ... or just the 0.1 power.
The right side of the equation becomes just C, and the left side of the equation which is:
.
{{{(0.5)^(0.1)}}}
.
equals 0.933032991
.
Substituting this value which is specific to the situation in New York harbor makes the
equation a little more specific as:
.
{{{I = I[o]*(0.933032991^x)}}}
.
With this equation you can solve for the Intensity (I) at any level if you are given the
intensity at the surface,{{{I[o]}}}, and the value of x (the depth in cm???).
.
Hope this helps you get started on the problem. With this answer, your problem will drop of
the list. If you need additional help, you'll need to repost it, and maybe another tutor
will pick it up and be able to give you more assistance than I did. However, if you repost,
it would help if you would define x, C, and Photic Zone. Plus any other information
that you might have about the problem.
.
Good luck and happy holidays to you and yours ...
.
```