College Algebra, Chapter 5, 5.2, Section 5.2, Problem 82

Suppose that a spectrophotometer measures the concentration of a sample dissolved in water by shining a light through it and recording the amount of light that emerges. In other words, if we know the amount of light that is absorbed, we can calculate the concentration of the sample. For a certain substance the concentration (in moles/liter) is found by using the formula

$\displaystyle C = -2500 \ln \left( \frac{I}{I_0} \right)$

where $I_0$ is the intensity of the incident light and $I$ is the intensity of light that emerges. Find the concentration of the substance if the intensity of $I$ is $70 \%$ of $I_0$, then

$I = 07 I_0$

So,


$
\begin{equation}
\begin{aligned}

C =& -2500 \ln \left( \frac{0.7 \cancel{I_0}}{\cancel{I_0}} \right)
&& \text{Substitute } I = 0.7I_0
\\
\\
C =& -2500 \ln (0.7)
&& \text{Simplify}
\\
\\
C =& 891.69 \text{moles/liter}
&& \text{Concentration of the substance}
\end{aligned}
\end{equation}
$