Chapter 8.4, Problem 7MCQ

a.

To determine

To classify the polynomial.

Answer to Problem 7MCQ

Trinomial

Explanation of Solution

Given:

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

  

The population density of Nevada from 1930 to 2010 can be modelled by,

  $d=0.005n^2-0.142n+1$ where n is the number of years since 1930.

Concept used:

The polynomial can be classified with the number of terms in the expression:

Monomial − A polynomial with only one term

Binomial − A Polynomial with two terms

Trinomial − A polynomial with three terms

Using the above concept,

In the given equation, the number of terms is three resulting in a trinomial.

Conclusion:

The given expression is a trinomial.

b.

To determine

To determine the degree of the polynomial.

Answer to Problem 7MCQ

Degree of the polynomial is 2.

Explanation of Solution

Given:

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

  

The population density of Nevada from 1930 to 2010 can be modelled by,

  $d=0.005n^2-0.142n+1$ where n is the number of years since 1930.

Concept used:

Degree of the polynomial is the highest power of the terms in the polynomial.

In the given expression the term with highest power is 0. 005n² . The highest power is 2.

Therefore, the degree of the polynomial is 2.

Conclusion:

The degree of the polynomial is 2.

c.

To determine

To predict the density of population in 2020 and 2030.

Answer to Problem 7MCQ

In 2020, 28.72 people per square mile.

In 2030, 36.8 people per square mile.

Explanation of Solution

Given:

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

  

The population density of Nevada from 1930 to 2010 can be modelled by,

  $d=0.005n^2-0.142n+1$ where n is the number of years since 1930.

Calculation:

The year 2020 is 90 years after 1930.

Let n = 90.

Substituting the value of t in $d=0.005n^2-0.142n+1,$

  $\begin{array}{l}$ d=0.005{(90)}^2-0.142(90)+1$d=0.005(8100)-0.142(90)+1\\ d=40.5-12.78+1\\ d=28.72\end{array}$

The year 2030 is 100 years after 1930.

Let n = 100.

  $\begin{array}{l}$ d=0.005{(100)}^2-0.142(100)+1$d=0.005(10000)-0.142(100)+1\\ d=50-14.2+1\\ d=36.8\end{array}$

Conclusion:

Therefore, the density of population in 2020 is 28.72 people per square mile and the density of population in 2030 is 36.8 people per square mile.

d.

To determine

To explain the mathematical practise used.

Explanation of Solution

The mathematical practised used is substitution.

Substituting the known values to find the unknown value.