- #1
dragonblood
- 22
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I have a problem with an exponential function. I am wondering if an exact solution is possible, or if I have to write the solution as a logarithm of an unknown.
A formula says that [tex]E(z)=E(0)^{-kz}[/tex], where E is light intensity and z is depth in water. My objective is to find the constant k. I also know that [tex]E(3)=0.01E(0)[/tex].
I have tried to solve for k in the following way:
[tex]E(3)=0.01E(0)[/tex]
[tex]E(3)=100E(3)^{-3k}[/tex]
[tex]\ln |0.01E(3)|=-3k \ln|E(3)|[/tex]
I realize that all values except for k is a constant, however, I do not know the value of E, and my question is: Are there any ways to eliminate E(3) from the equation, leaving k=numerical constant?
-dragonblood
A formula says that [tex]E(z)=E(0)^{-kz}[/tex], where E is light intensity and z is depth in water. My objective is to find the constant k. I also know that [tex]E(3)=0.01E(0)[/tex].
I have tried to solve for k in the following way:
[tex]E(3)=0.01E(0)[/tex]
[tex]E(3)=100E(3)^{-3k}[/tex]
[tex]\ln |0.01E(3)|=-3k \ln|E(3)|[/tex]
I realize that all values except for k is a constant, however, I do not know the value of E, and my question is: Are there any ways to eliminate E(3) from the equation, leaving k=numerical constant?
-dragonblood