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When 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...

R(x) = √13 + 7x^0.4 / 1 + 4x^0.4

First I need to Find R(1), R(10), and R(100). Then I need to make a table of the values of R(x).

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Is this what you mean? $$R(x) = \sqrt{13 + \dfrac{7x^{0.4}}{1 + 4x^{0.4}}}$$ –  Richard Sullivan Sep 25 '12 at 13:16
    
That's exactly what I meant. Thank you. –  Brandt Sep 25 '12 at 16:59
    
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2 Answers

up vote 1 down vote accepted

$R(x)=\sqrt{\frac{13+7x^{0.4}}{1+4x^{0.4}}}\Rightarrow R(1)=2,\;R(10)=1.66383,\;R(100)=1.47606$

$\begin{array}{|l|c|c|}\hline\color{Red}x & 1&10&100\\\rm \color{Orange}{R(x)}&\hline 2&1.66383&1.47606\\\hline\end{array}$

$\begin{array}{|l|l|}\hline\color{Red}x &\color{Orange}{\rm R(x)}\\\hline 1&2\\\hline10&1.66383\\\hline100&1.47606\\\hline 250 &1.43203\\\hline700&1.39679\\\hline1000&1.38734\\\hline\end{array}$

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Okay, I worked the equation portion out and came up with the same answers, but I'm having some difficulty filling in the chart. We were given a column titled ‘x’ that listed the numbers 1, 10, 100, 250, 700 and 1000. And a second column titled ‘R(x)’ where we were asked to fill in the values of R(x). My question is how exactly do I come up with those values? Am I supposed to plug in my original answers somewhere? –  Brandt Sep 25 '12 at 17:22
    
I added an extra table, you actually plug in the x values in the R(x) formula and use a computer. –  Papadopoulos Geοrgios Sep 25 '12 at 17:42
    
Alright, thanks. I used my graphing calculator to plug in the x values and came up with the same answers. Thanks again! –  Brandt Sep 25 '12 at 17:53
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$R(x) =\sqrt{13} + \fbox{7$x^{0.4}/1$} + 4x^{0.4}$, can you clarify the boxed formula? Is it $7x^{\frac{0.4}{1}}\;\;or\;\;\frac{7x^{0.4}}{1}$ or something else?

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Sorry about that. 13 + 7x^0.4 is divided by 1 + 4x^0.4 in this particular equation. –  Brandt Sep 25 '12 at 13:05
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