Chapter 6.1, Problem 66E

a.

To determine

To find: the model representing the population as a function of number of years since 1970.

Answer to Problem 66E

  $y=102x^2-505x+18430$

Explanation of Solution

Given information:

The table shown below represents the data of population growth for Forsythe Country over the time.

Year	1970	1980	1990	1998
Population	17000	28000	44000	86000

Calculation:

Use graphing calculator to model the given condition. The steps involved are as follows:

1. Select stat mode using initial year (1970) as 0. Enter the data from the table as shown below.

  

2. Select the graph scatter points and from the menu to get the scattered plot as follows:

  

3. Calculate the quadratic regression as follows:

  

The quadratic equation obtained is $y=102x^2-505x+18430$ . Here x is the number of years from 1970 and y is the population number.

b.

To determine

To predict: the population in year 2020 by using the model.

Answer to Problem 66E

248180

Explanation of Solution

Given information:

The table shown below represents the data of population growth for Forsythe Country over the time.

Year	1970	1980	1990	1998
Population	17000	28000	44000	86000

Calculation:

The equation of the function evaluated in part a. is as follows:

  $y=102x^2-505x+18430$ .

Since 2020 is 50 years from 1970, so put $x=50$ in the equation and solve y as shown below.

  $\begin{array}{c}y=102{\left(50\right)}^2-505\left(50\right)+18430\\ =255000-25250+18430\\ =248180\end{array}$

Thus the predicted population in year 2020 will be $248180$ .