Chapter 1.10, Problem 72E

(a)

To determine

To plot: the data points and the model in the same viewing window.

Explanation of Solution

Given information:

The ordered pairs below give the intensities $y$ of the light measured by a light probe located $x$ centimeters from a light source.

  $\begin{array}{l}\left(30,0.1881\right)\left(38,0.1172\right)\left(46,0.0775\right)\\ \left(34,0.15443\right)\left(42,0.0998\right)\left(50,0.0645\right)\end{array}$

A mode that approximates the data is $y=171.33/x^2$ .

Calculation:

Use a graphing utility to plot the data points and the model in the same viewing window:

  

(b)

To determine

To approximate: the light intensity 25 centimeters from the light source.

Answer to Problem 72E

The model to approximate 0.274128 microwatts per square centimeters is the light intensity 25 centimeters from the light source.

Explanation of Solution

Calculation:

Use the model to approximate the light intensity 25 centimeters from the light source and substitute the value $x=25$ into the model and have

  $\begin{array}{l}y=\frac{171.33}{x^2}\text{the}\text{inverse}\text{variation}\\ y=\frac{171.33}{{\left(25\right)}^2}\text{Substitute}\text{the}\text{value}\\ y=0.274128\text{Simplify}\end{array}$

Thus, use the model to approximate 0.274128 microwatts per square centimeters is the light intensity 25 centimeters from the light source.