Question

Steadia is an island which experienced approximately linear population growth from 1950 to 2000. On the other hand, Randomian has experienced some turmoil more recently and did not experience linear nor near-linear growth. a. The table gives the population of these two countries, in millions. Does country A or country B represent the population of Steadia? Enter just the letter above of the country in the blank (A or B). _______ B. What is the approximate rate of change of the linear function? ______ C. Estimate the population of Steadia in 1988. ________ million people

Answer 1

Given a table represents the population of these two countries, in millions.

We will find which country represents the linear growth

So, we will find the difference between the consecutive population for the two countries:

For country A:

The differcne between the consecuitive years will be as follows:

9.9 - 7.7 = 2.2

12.4 - 9.9 = 2.5

14.7 - 12.4 = 2.3

16.9 - 14.7 = 2.2

18.8 - 16.9 = 1.9

For country B:

10.3 - 7.9 = 2.4

12.9 - 10.3 = 2.6

14.7 - 12.9 = 1.8

14 - 14.7 = -0.7

20.3 - 14.7 = 5.6

When we compare the results of the countries, we can deduce that the linear growth is for country A

So, the answer of part a) country A

B. What is the approximate rate of change of the linear function?

We will find the average of the differences calculated at part (a)

So, the average will be =

$\frac{2.2+2.5+2.3+2.2+1.9}{5}=2.22$

So, the approximate rate of change will be = 2.22 million per 10 years

= 0.222 million per year

C. Estimate the population of Steadia in 1988.

The population will be as follows:

$14.7+0.222\times8=14.7+1.776=16.476$

So, the population = 16.476 million people