To solve these types of questions, we will use the formula for the average rate of change, which is defined as:
[tex]\[
\text{Average rate of change} = \frac{\text{Change in sales}}{\text{Change in time}}
\][/tex]
Let's solve each part step-by-step.
### Part (a): Average rate of change between 2018 and 2019
1. Identify the sales values for the years 2018 and 2019 from the table:
- Sales in 2018: [tex]\( 269 \)[/tex] million dollars
- Sales in 2019: [tex]\( 284 \)[/tex] million dollars
2. Calculate the change in sales and the change in time:
- Change in sales: [tex]\( 284 - 269 = 15 \)[/tex] million dollars
- Change in time: [tex]\( 2019 - 2018 = 1 \)[/tex] year
3. Apply the formula:
[tex]\[
\text{Average rate of change} = \frac{15 \text{ million dollars}}{1 \text{ year}} = 15 \text{ million dollars/year}
\][/tex]
Therefore, the average rate of change of annual sales between 2018 and 2019 is:
[tex]\[ \boxed{15} \text{ million dollars/year} \][/tex]
### Part (b): Average rate of change between 2018 and 2022
1. Identify the sales values for the years 2018 and 2022 from the table:
- Sales in 2018: [tex]\( 269 \)[/tex] million dollars
- Sales in 2022: [tex]\( 269 \)[/tex] million dollars
2. Calculate the change in sales and the change in time:
- Change in sales: [tex]\( 269 - 269 = 0 \)[/tex] million dollars
- Change in time: [tex]\( 2022 - 2018 = 4 \)[/tex] years
3. Apply the formula:
[tex]\[
\text{Average rate of change} = \frac{0 \text{ million dollars}}{4 \text{ years}} = 0 \text{ million dollars/year}
\][/tex]
Therefore, the average rate of change of annual sales between 2018 and 2022 is:
[tex]\[ \boxed{0} \text{ million dollars/year} \][/tex]
