Chapter 6.8, Problem 8STP

To determine

To calculate: Evaluate $P\left(20\right)$ to estimate the population of the country in $1980$ .

The function $P\left(x\right)=-0.000047x^2+0.027x+3$ it is used to approximate the population of Ling’ s home country between $1960\text{ and }2000$ , domain of the function $x$ represented the number of the years.

Answer to Problem 8STP

The $P\left(20\right)$ evaluation population of the country in $1980$ : $P\left(20\right)=3.5212$ , option $J$ is correct.

Explanation of Solution

Given information:

The function $P\left(x\right)=-0.000047x^2+0.027x+3$ it is used to approximate the population of Ling’ s home country between $1960\text{ and }2000$ , domain of the function $x$ represented the number of the years.

Since, $1960$ , and $P$ is given in millions of people. Evaluate $P\left(20\right)$ to estimate the population of the country in $1980$ .

The options are:

  $\begin{array}{l}\text{F about 2 millions people H about 2}\text{.5 million people }\\ \text{G about 3 millions people J about 3}\text{.5 million people }\end{array}$

Calculation:

Considered the statement, The function $P\left(x\right)=-0.000047x^2+0.027x+3$ it is used to approximate the population of Ling’ s home country between $1960\text{ and }2000$ , domain of the function $x$ represented the number of the years.

Since, $1960$ , and $P$ is given in millions of people. Evaluate $P\left(20\right)$ to estimate the population of the country in $1980$ .

The function of approximate population of Ling’s home country:

  $P\left(x\right)=-0.000047x^2+0.027x+3$

Enter $20$ for $x$ ,

  $-0.000047\times {\left(20\right)}^2+0.027\times 20+3$

Square the $20$ as:

  $P\left(20\right)=-0.000047\times 400+0.027\times 20+3$

Now multiply all the terms:

  $\begin{array}{l}P\left(20\right)=-0.0188+0.54+3\\ P\left(20\right)=3.5212\end{array}$

Hence, the $P\left(20\right)$ evaluation population of the country in $1980$ : $P\left(20\right)=3.5212$ , option $J$ is correct.