Question

Population of a city in the years 2005 and 2010 are 1,35,000 and 1,45,000 respectively. Find the approximate population in the year 2015. (assuming that the growth of population is constant)

Answer 1

Let us choose the year along the x-axis and the population of the city along the y-axis.

Given In the year 2005 population is 1,35,000

The corresponding point is (2005, 1,35,000)

In the year 2010, population is 1,45,000

The corresponding point is (2010, 1,45,000)

Let Y denote the year and P denote the population.

The relation connecting Y and P is the equation of the straight line joining the points (2005, 1,35,000) and (2010, 1,45,000)

`("Y" - 2005)/(2010 - 2005) = ("P" - 135000)/(1445000 - 135 000)`

`("Y" - 2005)/5 = ("P" - 135000)/10000`

When y = 2015

2015 – 2005 = `("P" - 135000)/2000`

10 = `("P" - 135000)/2000`

P = 135000 + 10 × 2000

P = 135000 + 20000 = 155000

∴ The population in the year 2015 is 1,55,000