Chapter 3.4, Problem 29AYU

(a)

To determine

To graph:

The scatter plot and describes the relation between the age and percentage.

Explanation of Solution

Given information:

Age, x	Per. Without a high school diploma, p
$30$	$13.3$
$40$	$11.6$
$50$	$10.9$
$60$	$13.7$
$70$	$22.3$
$80$	$30.2$

The data represents the percentage of the U.S. population whose age is $x$ .

Graph:

  

Interpretation:

By using the graphing utility, the scatter plot is as drawn.

Above scatter plot describes the data of percentage of the U.S. population whose age is $x$ .

The relation is quadratic function appears to exist between age and percentage of the population without a high school diploma.

(b)

To determine

To calculate:

The linear or quadratic model based on (a).

Answer to Problem 29AYU

A linear or quadratic model that describes the relation between age and percentage of the population that do not have a high school diploma is $P\left(a\right)=0.015a^2-1.33a+39.8$ .

Explanation of Solution

Given information:

The data represents the percentage of the U.S. population whose age is $x$ .

Age, x	Per. Without a high school diploma, p
$30$	$13.3$
$40$	$11.6$
$50$	$10.9$
$60$	$13.7$
$70$	$22.3$
$80$	$30.2$

Calculation:

  $P\left(a\right)=0.015a^2-1.33a+39.8$

  

Hence, the function is $P\left(a\right)=0.015a^2-1.33a+39.8$ .

(c)

To determine

To Calculate:

The percentage of $35$ years old

Answer to Problem 29AYU

The percentage of $35$ years old is $P\left(35\right)=11.6$ .

Explanation of Solution

Given information:

The data represents the percentage of the U.S. population whose age is $x$ .

Age, x	Per. Without a high school diploma, p
$30$	$13.3$
$40$	$11.6$
$50$	$10.9$
$60$	$13.7$
$70$	$22.3$
$80$	$30.2$

Calculation:

  $\begin{array}{l}P\left(a\right)=0.015a^2-1.33a+39.8\\ P\left(35\right)=0.015{\left(35\right)}^2-1.33\left(35\right)+39.8\\ P\left(35\right)=11.6\end{array}$

Hence, the percentage is $P\left(35\right)=11.6$ .