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- anonymous

PLEASE HELP!!!!
The photic zone describes the region in which microscopic plant life receive enough light to survive. The photic zone goes to a depth where about 1% of the surface light still remains. Find the depth of the photic zone if the intensity of light (L) at a depth (d) in meters is given by L=L0e^(-0.028d), where L0 is the intensity of surface light. You may use the graphing part of your calculator for this question.
Possible answers are:
a. 124 m
b. 134 m
c. 144 m
d. 154 m
e. 164 m

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- anonymous

- schrodinger

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- anonymous

I know you can use your calculator to find it but I have no idea how!!!

- anonymous

L=100 per cent
LO=1 per cent

- anonymous

Ok, so how can I use that to solve? :( do I plug 0.01e^(-0.028x) into my calculator???

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- anonymous

You have an equation, the given, as they say. It has three unknowns -- not good. We have found two of the unknowns -- better. So now with one unknown you can solve for d.\[100percent=1percente ^{-0.028d}\]

- anonymous

That makes much more sense, thank you. However im not so great at solving with exponents. How do I solve? This is how I would do it but I have noooo idea.
100 10,000
---- = -0.028d ===> ------- = d ===> d= -357142.86
0.01 -0.028
I know its wrong but idk why :(

- anonymous

You lost your e. You can't just arbitrarily take away your e. The plants would die from lack of sunlight.

- anonymous

100
---- = -0.028d should it start like that?
0.01e

- anonymous

\[100=e ^{-0.028d}\]You have to use logarithms. Who knew marine biology was so much work.\[\ln 100=\ln e ^{-0.028d}\]

- anonymous

So we just forget about the 0.01?
does it turn into
100
------ = d? that gives me d=-3571.43
-0.028

- anonymous

There is no 0.01. The percentage signs cancel leaves 100 over one which is 100

- anonymous

Ok, but I still solved and got -3571.43, which is not one of my answers. I dont understand!

- anonymous

May be you did something wrong\[\ln 100=- 0.028d \ln e \]

- anonymous

which gives me ln (100/-0.028)???? Im sorry I dont understand how to do these at all and I need to solve this problem

- anonymous

You have the ability to find ln 100 and ln e on your calculator

- anonymous

lne = 1 and ln100 =4.6, correct???

- anonymous

yes

- anonymous

so then I take 4.6/-0.028= -164.28, correct?

- anonymous

Yes but depth is always positive, so absolute value (erase negative sign)

- anonymous

So the answer is E, 164 m? Thanks

- anonymous

You're pretty good.

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