A new employee at an exciting new software company starts with a salary of $\$50,000$ and is promised that at the end of each year her salary will be double her salary of the previous year, with an extra increment of $\$10,000$ for each year she has been with the company.
- Construct a recurrence relation for her salary for her $n^{\text{th}}$ year of employment.
- Solve this recurrence relation to find her salary for her $n^{\text{th}}$ year of employment.
