Question

Got stuck half way please help :(
The intensity of light (d) metres below the surface of the sea can be modelled by the equation I=Ioe^(-kd). Divers in the Sea if Loga have found that the intensity of light is halved when a diver is 5m below the surface of the water.
a) Find value of k
-I found the value of k by first making d=0 and then d=-5 Now the equation is I=Ioe^(-0.1386d).
**b) Find the percentage of light available at a depth of 10 metres... im stuck on this

Answer 1

am i looking at simultaneous equations possibly?
I=Ioe^(-0.1386*-5)
I=Ioe^(-0.1386*-10)

Answer 2

answer is 25%

Answer 3

Did you work it out or would you like an explanation?

Answer 4

i would like an explanation please, am i on the right track with simultaneous equations?

Answer 5

This is a tricky question simply because we don't know what the initial intensity of light is. In fact, we'll never find out :(
However, the question is asking us for a PERCENTAGE of light left.
For starters though, I don't think your k value is correct. I got positive 0.1386... instead of negative. Did you get k = ln(0.5)/-5 ?

Ok, so your idea of simultaneous equations was clever but unfortunately doesn't work in this situation. What we have to do is similar to what we did in part a.
In part a, you probably did something like I = Io/2, right?
Well now, that can be written is I = Io * 50%.
What we should be doing is letting I = Io * P, where P is the percentage we want to end up with.
Let me know if that helps.

Answer 6

for my k value i got 0.1386 but because the original equation said -kd .. i wrote it like that.. hope that is okay

Answer 7

Actually you wrote I=Ioe^(-0.1386*-5), which implies you used the negative, but that's ok because I just realised you were using negative numbers for depth. If d was height, negative numbers would represent depth, but it doesn't really matter.

Did the rest help? Letting I = Io * P?

Answer 8

Io=(Io*e^(-0.1386*-10)/2) *P

Answer 9

im getting 50% where as answer is 25%

Answer 10

wait...what i did is not right

Answer 11

Where did that /2 come from?
Ok I'll show you my working:
I = Io * P
Io*P = Ioe^(-10*k) [I have k saved in my calculator]
Divide both sides by Io and you get
P = e^(-10*k)

Answer 12

Also, be careful with your negatives

Answer 13

i realised i missed a part of the equation out when i was working it out

Answer 14

i got it :) Thanks so much I really appreciate it

Answer 15

No worries, happy to help