Question

The population data for a certain country are as follows: Year 2012 2013 2014 2015 2016 2017 Population (millions) 10 10.9 11.7 12.6 13.8 14.9 Obtain a function that describes these data. Plot the function and the data on the same plot. Estimate when the population will be double its 2004 size.

Answer 1

Function is y = 0.974x + 2.086

On 2006, the population will be double its 2004 size.

Explanation:

Let x represents the number of years and y represents the population after x years,

Also, suppose reference year is 2004,

Then, the table would be,

x 8 9 10 11 12 13

y 10 10.9 11.7 12.6 13.8 14.9

Since, the value of y is increasing approximately linearly with increasing the value of x,

Thus, a linear function will best describe the given points,

For finding the equation we will follow the following steps,

Step 1 : Make the table on the excel,

Step 2 : Select the table,

Step 3 : insert the scatter plot ( scatter plot with smooth lines )

Step 4 : choose the option 'add trendiness'

Step 5 : Mark the option 'display equation on the chart'.

By these steps we will get y = 0.974x + 2.086

For 2004, x = 0,

y = 0.974(0) + 2.086

y = 2.086

Hence, the population on 2004 is 2.086 millions,

If y = 4.172,

4.172 = 0.974x + 2.086

2.086 = 0.974x

⇒ x = 2.14168377823 ≈ 2,

Therefore, on 2006, the population will be double its 2004 size.