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Pupil Size 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$$R(x)=\sqrt{\frac{13+7 x^{0.4}}{1+4 x^{0.4}}}$$

where $R$ is measured in millimeters and $x$ is measured in appropriate units of brightness.(a) Find $R(1), R(10),$ and $R(100)$(b) Make a table of values of $R(x)$

(a) $R(1)=2, R(10)=1.66383$ and $R(100)=1.476$(b) $\begin{array}{|c|c|}\hline x & {R(x)} \\ \hline 1 & {2} \\ \hline 20 & {1.59344} \\ \hline 40 & {1.53568} \\ \hline 60 & {1.50714} \\ \hline 80 & {1.489} \\ \hline 100 & {1.446} \\ \hline\end{array}$

Algebra

Chapter 3

Functions

Section 1

What Is a Function?

Campbell University

Baylor University

Idaho State University

Lectures

01:32

In mathematics, the absolu…

01:11

03:51

Pupil size When the bright…

04:01

Pupil Size When the bright…

05:34

02:22

Sensitivity of the eye to …

02:34

It $ R $ denotes the react…

Suppose that the size of t…

05:06

The size of an animal'…

0:00

Light enters the eye throu…

02:26

Astronomers can use the br…

03:53

Human vision sensitivity T…

Okay, so we're given our function for our vex. That's equal to the square root function. And I we want to find values from 1 to 100. So it's put that into our calculator. So we have the square roots, and that's of that's going to be 13 and plus seven times are ex term. In this case, that's going to be people or and that's to the power of zero points for. And then we're gonna divide this by way one plus four and then before that's going too many times before to the power of 0.4. So this was just too, and we want to find this from 10 or for a remaining expellees. So it's this poor sound, so these are our values.

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In mathematics, the absolute value or modulus |x| of a real number x is its …

Pupil size When the brightness $x$ of a light source is increased, the eye r…

Pupil Size When the brightness $x$ of a light source is increased, the eye r…

Pupil Size When the brightness $x$ of a light source isincreased, the ey…

Sensitivity of the eye to brightness If $R$ denotes the reaction of the body…

It $ R $ denotes the reaction of the body to some stimulus of strength $ x. …

Suppose that the size of the pupil of an animal is given by $f(x)$ (mm), whe…

The size of an animal's pupils expand and contract depending on the amo…

Light enters the eye through the pupil and strikes the retina, where photore…

Astronomers can use the brightness of two light sources, such as stars, to c…

Human vision sensitivity To see an object with the unaided eye, the light in…

04:40

Graph the function in each of the given viewing rectangles, and select the o…

00:32

Find all solutions of the equation, and express them in the form $a+b i$…

01:07

$9-18$ m function $f$ is given. (a) Use a graphing calculator to draw the gr…

02:00

A function is given. Determine the average rate of change of the function be…

02:02

Evaluate the expression and write the result in the form a bi.$$(2-…

01:03

$21-44$ . Sketch the graph of the function, not by plotting points, but by s…

01:12

$31-42$ . Solve the equation both algebraically and graphically. $$\…

00:27

In Example 6 we found two solutions of the equation $x^{3}-6 x^{2}+9 x=\sqrt…

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