Chapter 3.3, Problem 60E

Solution

To calculate: The intensity of the light at a depth of $\text{30}\text{ft}\text{.}$ .

The intensity of the light at a depth of $30ft$ is about $10.2$ lumens.

Given information: The Beer-Lambert Law of Absorption applied to Lake Erie states that the light intensity $I$ (in lumens), at a depth of $x$ feet, satisfies the equation

  $\log \frac{I}{12}=-0.00235x$

Calculation:

The light intensity $I$ (in lumens), at a depth of $x$ feet, satisfies the equation-

  $\log \frac{I}{12}=-0.00235x$

To find the intensity of the light at a depth of $30ft$ , Substitute $30$ for $x$ in the above equation-

  $\begin{array}{c}\log \frac{I}{12}=-0.00235(30)\\ \log \frac{I}{12}=-0.0705\end{array}$

Convert the equation in exponential form:

  $\begin{array}{c}\frac{I}{12}={10}^{-0.0705}\\ \frac{I}{12}\approx 0.8501\\ I\approx 12\times 0.8501\\ I\approx 10.2\end{array}$

Thus, The intensity of the light at a depth of $30ft$ is about $10.2$ lumens.