Chapter 7, Problem 29MCQ

(a)

To determine

To find:The type of polynomial.

Answer to Problem 29MCQ

The equation $d=0.005y^2-0.127y+1$ is the quadratic type of polynomial.

Explanation of Solution

Given information:

Giventhe population density $d$ of Nevada from $1930$ to $2000$ can be modeled $d=0.005y^2-0.127y+1$ . Where $y$ is the number of years since $1930$ .

Year	Years Since $1930$	People/Square Mile
$1930$	$0$	$0.8$
$1960$	$30$	$2.6$
$1980$	$50$	$7.3$
$1990$	$60$	$10.9$
$2000$	$70$	$18.2$

Calculation:

Consider the table

The table shows the population density for Nevada for various years.

  $d=0.005y^2-0.127y+1$ has the $2$ terms.

Therefore, the equation $d=0.005y^2-0.127y+1$ is the quadratic type of polynomial.

(b)

To determine

To find:Thedegree of the polynomial.

Answer to Problem 29MCQ

The degree of the polynomial is $2$

Explanation of Solution

Given information:

Given the population density $d$ of Nevada from $1930$ to $2000$ can be modeled $d=0.005y^2-0.127y+1$ . Where $y$ is the number of years since $1930$ .

Calculation:

The degree of the polynomial is the highest degree of the terms.

Therefore, thedegree of the polynomial is $2$ .

(c)

To determine

To find: The population density of Nevada for $2020$

Answer to Problem 29MCQ

The population density of Nevada for $2030$ is $38.3$ .

Explanation of Solution

Given information:

Given the population density $d$ of Nevada from $1930$ to $2000$ can be modeled $d=0.005y^2-0.127y+1$ . Where $y$ is the number of years since $1930$ .

Calculation:

The population density of Nevada for $2020$ .

  $2020$ is $90$ years after.

Substitute the value

  $\begin{array}{c}d=0.005y^2-0.127y+1\\ d=0.005{\left(90\right)}^2-0.127\left(90\right)+1\\ d=0.005\times 8100-11.43+1\\ d=40.5-10.43\\ d=30.07\end{array}$

Therefore, the population density of Nevada for $2020$ is $30.07$ .

(d)

To determine

To find: The population density of Nevada for $2030$ .

Answer to Problem 29MCQ

The population density of Nevada for $2030$ is $38.3$ .

Explanation of Solution

Given information:

Given that for area of circle use $A=\pi r^2$ and for area of square use $A=s^2$ .

Calculation:

The population density of Nevada for $2030$ .

  $2030$ is $100$ years after.

Substitute the value

  $\begin{array}{c}d=0.005y^2-0.127y+1\\ d=0.005{\left(100\right)}^2-0.127\left(100\right)+1\\ d=0.005\times 10,000-12.7+1\\ d=50-11.7\\ d=38.3\end{array}$

Therefore, the population density of Nevada for $2030$ is $38.3$ .