1. ## function of intensity

the intensity of light, in lumens, passing through a liquid with an absorption coefficent of 0.2 is given by I(d)=100e^-0.2d, where d is the depth, in metres.
a)what is the intensity of light passing through 5m of this liquid?
b) how many metres must the light travel before the intensity is reduced to 1% of the original intensity?

2. Originally Posted by anitha
the intensity of light, in lumens, passing through a liquid with an absorption coefficent of 0.2 is given by I(d)=100e^-0.2d, where d is the depth, in metres.
a)what is the intensity of light passing through 5m of this liquid?
b) how many metres must the light travel before the intensity is reduced to 1% of the original intensity?
For part (a), use a calculator:

$\displaystyle I(5)=100e^{-0.2(5)}=\dots$

For part (b):

If the equation is $\displaystyle I=I_0e^{-\alpha d}$

where

$\displaystyle I$ is the current intensity,
$\displaystyle I_0$ is the original intensity, and
$\displaystyle \alpha$ is the absorption constant,

we want to find the distance $\displaystyle d$ where the current intensity is 1% of the original intensity, meaning that $\displaystyle \frac{I}{I_0}=.01$

So the equation we want to solve is $\displaystyle .01=e^{-0.2d}$

Taking the natural log of both sides gives us $\displaystyle \ln(.01)=-0.2d\implies d=\frac{2\ln(10)}{0.2}\approx\dots$

I hope this makes sense!

--Chris