Question

In 2010, the population of a city was 170,000. From 2010 to 2015, the population grew by 4.5%. From 2015 to 2020, it fell by 3.3%. To the nearest 100 people, what was the population in 2020?

Answer 1

Given a percentage of change we can calculate the final population by the end of a period with the following formula:

P = P0 + xP0

Where P is the final population, P0 is the initial population at the beginning of the period and x is the percentage of change, if the population grew x will be a positive value and if the population fell x will be a negative value.

For the period 2010 to 2015, the population was initially 170,000 and it grew by a 4.5%. Then by replacing 0.045 for x (4.5/100) and 170000 for P0, we get:

P2015 = 170000 + 0.045×170000 = 177650

From 2015 the population decay by 3.3%, then we can calculate the population by 2020 to get:

P2020 = 177650 + 177650×(-0.033) = 171787

Then, rounding to the nearest 100 people we get 171,800