College Algebra, Chapter 3, 3.1, Section 3.1, Problem 74

Suppose the brightness $x$ of a light source is increased, the eye reacts by decreasing the radius $R$ of the pupil. The dependence of $R$ on $x$ is given by the function
$\displaystyle R(x) = \sqrt{\frac{13+7x^{0.4}}{1 + 4x^{0.4}}}$
a.) Find $R(1), R(10)$ and $R(100)$
For $R(1)$,

$
\begin{equation}
\begin{aligned}
R(1) &= \sqrt{\frac{13+7(1)^{0.4}}{1 + 4(1)^{0.4}}}\\
\\
&= 2
\end{aligned}
\end{equation}
$


For $R(10)$,

$
\begin{equation}
\begin{aligned}
R(10) &= \sqrt{\frac{13+7(10)^{0.4}}{1 + 4(10)^{0.4}}}\\
\\
&= 1.66
\end{aligned}
\end{equation}
$

For $R(100)$,

$
\begin{equation}
\begin{aligned}
R(10) &= \sqrt{\frac{13+7(100)^{0.4}}{1 + 4(100)^{0.4}}}\\
\\
&= 1.48
\end{aligned}
\end{equation}
$


b.) Make a table of values of $R(x)$

$
\begin{array}{|c|c|}
\hline\\
x & R(x)\\
\hline\\
1 & 2 \\
\\
10 & 1.66\\
\\
100 & 1.48\\
\\
1000 & 1.39\\
\\
10000 & 1.35\\
\\
\hline
\end{array}
$