anonymous
  • 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
Mathematics
schrodinger
  • schrodinger
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anonymous
  • anonymous
I know you can use your calculator to find it but I have no idea how!!!
anonymous
  • anonymous
L=100 per cent LO=1 per cent
anonymous
  • 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
  • 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
  • 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
  • anonymous
You lost your e. You can't just arbitrarily take away your e. The plants would die from lack of sunlight.
anonymous
  • anonymous
100 ---- = -0.028d should it start like that? 0.01e
anonymous
  • 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
  • anonymous
So we just forget about the 0.01? does it turn into 100 ------ = d? that gives me d=-3571.43 -0.028
anonymous
  • anonymous
There is no 0.01. The percentage signs cancel leaves 100 over one which is 100
anonymous
  • anonymous
Ok, but I still solved and got -3571.43, which is not one of my answers. I dont understand!
anonymous
  • anonymous
May be you did something wrong\[\ln 100=- 0.028d \ln e \]
anonymous
  • 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
  • anonymous
You have the ability to find ln 100 and ln e on your calculator
anonymous
  • anonymous
lne = 1 and ln100 =4.6, correct???
anonymous
  • anonymous
yes
anonymous
  • anonymous
so then I take 4.6/-0.028= -164.28, correct?
anonymous
  • anonymous
Yes but depth is always positive, so absolute value (erase negative sign)
anonymous
  • anonymous
So the answer is E, 164 m? Thanks
anonymous
  • anonymous
You're pretty good.

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