Question

In 2010, the population of a city was 87,000. From 2010 to 2015, the population grew by 7.7%. From 2015 to 2020, it fell by 4.5%. To the nearest 100 people, what was the population in 2020?

Answer 1

The population of the city in 2020 was 89,500 to the nearest 100 people.

Explanation:

The original population in 2010 is 100%.

If the population is increased by 7.7% from 2010 to 2015, the total percentage in 2015 is 107.7% of the population in 2010.

Convert this to a decimal and multiply by the original population of 87,000 to find the population of the city in 2015.

`\begin{aligned}\implies \sf 107.7\%\;of\;87000&=\sf 1.077 * 87000\\&=\sf 93699\end{aligned}`

Therefore, the population of the city in 2015 was 93,699.

The population in 2015 is 100%.

If the population is decreased by 4.5% from 2015 to 2020, the total percentage in 2020 is 95.5% of the population in 2015.

Convert this to a decimal and multiply by the population in 2015 to find the population of the city in 2020.

`\begin{aligned}\implies \sf 95.5\%\;of\;93699&=\sf 0.955 * 93699\\&=\sf89482.545 \end{aligned}`

Therefore, the population of the city in 2020 was 89,500 to the nearest 100 people.