Answer:
(View Below)
Explanation:
a. Recursive formulas for calculating Josie's salary in the nth year for both companies:
**Company A:** In Company A, Josie's salary increases by a fixed amount each year, $4,000. The recursive formula for her salary in the nth year, denoted as S_A(n), can be written as:
S_A(n) = S_A(n-1) + $4,000
Where S_A(n-1) represents her salary in the previous (n-1) year.
**Company B:** In Company B, Josie's salary increases by a percentage (9%) of her previous year's salary. The recursive formula for her salary in the nth year, denoted as S_B(n), can be written as:
S_B(n) = S_B(n-1) + (0.09 * S_B(n-1))
Where S_B(n-1) represents her salary in the previous (n-1) year, and 0.09 represents a 9% increase.
b. To determine which company Josie should choose, we can compare the salary growth in both companies over time:
- In Company A, Josie's salary increases by a fixed amount ($4,000) each year. This means that her salary growth is predictable and linear.
- In Company B, Josie's salary increases by a percentage (9%) of her previous year's salary. This means that her salary growth is exponential, and it will grow at an increasing rate over time.
The choice between Company A and Company B depends on Josie's preferences and financial goals:
- If Josie values predictable and steady salary growth, Company A might be the better choice, as her salary increases by a fixed amount each year.
- If Josie is looking for potentially faster salary growth in the long run, Company B might be more appealing, as exponential growth can lead to larger salary increases over time.
Ultimately, the choice depends on Josie's personal preferences, financial priorities, and how comfortable she is with the predictability of salary increases in Company A versus the potentially more substantial increases in Company B.