Chapter 1.4, Problem 10MCQ

a.

To determine

To find: average annual rate of increase of population.

Answer to Problem 10MCQ

  $170823.7$ people per year

Explanation of Solution

Given information:

Population in 1990 = 6478216

Population by 2000 = 8186453

Let year be x and population be y.

Therefore, the points on line are as follows:

  $\begin{array}{l}\left(x_1,y_1\right)=\left(1990,6478216\right)\\ \left(x_2,y_2\right)=\left(2000,8186453\right)\end{array}$

Calculation

The equation slope is as follows:

  $m=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}$

Substitute the value in the above equation to get,

  $\begin{array}{c}m=\frac{\left(y_2-y_1\right)}{\left(x_2-x_1\right)}\\ =\frac{8186453-6478216}{2000-1990}\\ =\frac{1708237}{10}\\ =170823.7\end{array}$

Therefore, the average annual rate increase is $170823.7$ people per year.

b.

To determine

To find: equation that depicts the population change.

Answer to Problem 10MCQ

  $y=170823.7x-333460947$

Explanation of Solution

Given information:

  $\begin{array}{c}\left(x_1,y_1\right)=\left(1990,6478216\right)\\ \left(x_2,y_2\right)=\left(2000,8186453\right)\\ m=170823.7\end{array}$

Calculation

The slope intercept form is as follows:

  $y=mx+b$ … (1)

Substitute the value of m in equation (1) to evaluate b as shown below.

  $\begin{array}{c}6478216=\left(170823.7\right)\left(1990\right)+b\\ 6478216=339939163+b\\ b=6478216-339939163\\ =-333460947\end{array}$

Substitute the value of b and m in equation (1) and simply it as follows:

  $\begin{array}{l}y=\left(170823.7\right)x+\left(-333460947\right)\\ y=170823.7x-333460947\end{array}$

Therefore, the equation is $y=170823.7x-333460947$ .