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.

a) Construct a recurrence relation for her salary for her nth year of employment.

b) Solve this recurrence relation to find her salary for her nth year of employment.

Some linear recurrence relations that do not have constant coefficients can be systematically solved. This is the case for recurrence relations of the form f (n)an = g(n)an1 + h(n).