Question

In 2007, the population of Cleveland, Ohio was 440,358, and in 2017, it was 385,525 people. What is the absolute and relative change in Cleveland's population from 2007 to 2017?Round your answer for relative change to the nearest hundredth of a percent.Do not round until your final answer.

Answer 1

Step-by-step explanation

Let's assume that a certain quantity q increases or decreases until it reaches a value q'. Then the absolute change is given by:

`\Delta=q^(\prime)-q`

On the other hand the relative change is given by dividing the absolute change with the original value:

`R=(\Delta)/(q)=(q^(\prime)-q)/(q)`

In this case the original quantity is the population of Cleveland in 2007 and the increased/decreased quantity is the population of the city in 2017. Therefore we have q=440358 and q'=385525. Then the absolute change is:

`\Delta=q^(\prime)-q=385525-440358=-54833`

The relative change is given by:

`R=(q^(\prime)-q)/(q)=-(54833)/(440358)=-0.1245`

As a percent the relative change is:

`-0.1245\cdot100=-12.45\text{ \%}`

Answer

Then the answers are:

Absolute change: -54833

Relative change: -12.45%