Question: Emma earns a $39,000 salary in the first year of her career. Each year, she gets a 5% raise. How much does Emma earn in total in the first 11 years of her career? Round your final answer to the nearest thousand.

1. **State the problem:** Emma starts with a salary of $39000$ in the first year and receives a 5% raise each subsequent year. We want to find the total amount she earns over the first 11 years. 2. **Identify the formula:** This is a geometric series problem where the first term $a = 39000$ and the common ratio $r = 1 + 0.05 = 1.05$. The total earnings over $n$ years is given by the sum of a geometric series: $$S_n = a \frac{1-r^n}{1-r}$$ 3. **Apply the formula:** Here, $n = 11$, $a = 39000$, and $r = 1.05$. Calculate $r^n$: $$1.05^{11} \approx 1.71034$$ Calculate the sum: $$S_{11} = 39000 \times \frac{1 - 1.71034}{1 - 1.05} = 39000 \times \frac{1 - 1.71034}{-0.05}$$ 4. **Simplify the fraction:** $$\frac{1 - 1.71034}{-0.05} = \frac{-0.71034}{-0.05} = \cancel{\frac{-0.71034}{-0.05}} = 14.2068$$ 5. **Calculate total earnings:** $$S_{11} = 39000 \times 14.2068 = 554,665.2$$ 6. **Round the answer:** Rounded to the nearest thousand, Emma earns approximately $555000$ in total over the first 11 years. **Final answer:** $$\boxed{555000}$$