Logarithmic Problem: light intensity passing through water

[sail0r]

Ok. Here is a wordy one, but help would be much appreciated.

Light intensity behaves similarly to sound intensity. A large aquarium in a science centre holds various fish and plants. Most of the plants require a light intensity of 4.2 units for strong growth. Light intensity, I, passing through water can be modeled with I=10^(1-0.13x), where x is the depth of the water in metres. Use this equation to find the depth at which the plants will receive appropriate light.

I believe sound intensity is I=10log(I/Io)

Cheers

 

[arthur ohlsten]

Re: Logarithmic Problem

l=10^(1-.13x) let us rewrite the equation
l=10^1 / 10^.13x
10^.13x=10/l
but l=4.2
10^.13x =10/4.2
take logs of both sides
.13x= log 10 - log 4.2
x=[1-log 4.2] / .13 answer

Arthur

 

[fasteddie65]

Re: Logarithmic Problem

I = 10^(1 - 0.13x)
4.2 = 10^(1 - 0.13x)
log 4.2 = 1 - 0.13x
0.13x = 1 - log 4.2
0.13x = 0.3767...
x = 2.898...