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Question 9

SALARY The table shows the annual salary of a salesperson over time. Find the average rate of change over the given time interval. Interpret the results in context of this situation.
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average rate of change: ; From 2012 to 2017, the salesman's average rate of change in salary was an increase of $\mathrm{\$}$ per year.
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Step 1 ：The average rate of change is calculated by subtracting the initial value from the final value and then dividing by the number of years. In this case, the initial value is the salary in 2012 and the final value is the salary in 2017. The number of years is 2017 - 2012.

Step 2 ：Let's denote the initial salary as $initial\mathrm{\_}salary=\mathrm{\$}45000$, the final salary as $final\mathrm{\_}salary=\mathrm{\$}67500$, and the number of years as $years=5$.

Step 3 ：Calculate the average rate of change as $average\mathrm{\_}rate\mathrm{\_}of\mathrm{\_}change=\frac{final\mathrm{\_}salary-initial\mathrm{\_}salary}{years}$.

Step 4 ：Substitute the given values into the formula to get $average\mathrm{\_}rate\mathrm{\_}of\mathrm{\_}change=\frac{\mathrm{\$}67500-\mathrm{\$}45000}{5}=\mathrm{\$}4500.0$.

Step 5 ：Final Answer: The salesman's average rate of change in salary from 2012 to 2017 was an increase of $\boxed{{\displaystyle \mathrm{\$}4500}}$ per year.