In 2010, the population of Macon, GA was 153,159. In 2019, the population was 91,351. Which of the following expressions could be used to determine the average rate of change in population from 2010 to 2019?

(A) [tex]$\frac{153,159-91,351}{2019-2010}$[/tex]

(B) [tex]$\frac{91,351-153,159}{2019-2010}$[/tex]

(C) [tex]$\frac{153,159-91,351}{2010-2019}$[/tex]

(D) [tex]$\frac{2019-2010}{153,159-91,351}$[/tex]

To find the average rate of change in the population from 2010 to 2019, we need to use the formula for the average rate of change. The average rate of change can be calculated using the formula:

[tex]\[
\frac{\text{Change in population}}{\text{Change in time}}
\][/tex]

1. Determine the change in population:
- Population in 2010: 153,159
- Population in 2019: 91,351
- Change in population = Population in 2019 - Population in 2010
- Change in population = 91,351 - 153,159

2. Determine the change in time:
- Year in 2010: 2010
- Year in 2019: 2019
- Change in time = 2019 - 2010
- Change in time = 9 years

3. Calculate the average rate of change:
- Using the values we found:
- Average rate of change = [tex]$\frac{91,351 - 153,159}{2019 - 2010}$[/tex]
- Average rate of change = [tex]$\frac{91,351 - 153,159}{9}$[/tex]

After calculating, the numerical result for the average rate of change is:

[tex]\[
-6,867.56 \, \text{(approximately)}
\][/tex]

This means the population of Macon, GA decreased on average by about 6,868 people per year from 2010 to 2019.

The correct expression from the options provided is:

(B) [tex]$\frac{91,351-153,159}{2019-2010}$[/tex]