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 $R(x)$

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