Question
Collette works at a company that gives all its employees an annual cost-of-living pay raise. The function below can be used to determine Collette's salary in her nth year of working at the company.
Which of these statements about Collette's salary are true? Choose all that are correct.
A.
Collette's salary is $50,000 in her first year.
B.
Collette's salary is $51,035 in her first year.
C.
Collette's salary is $51,750 in her first year.
D.
After working at least one year at the company, Collette's salary is equal to last year's salary plus $1,035.
E.
After working at least one year at the company, Collette's salary is equal to last year's salary multiplied by 1.035.
F.
After working at least one year at the company, Collette's salary is equal to last year's salary multiplied by (n – 1).
Which of these statements about Collette's salary are true? Choose all that are correct.
A.
Collette's salary is $50,000 in her first year.
B.
Collette's salary is $51,035 in her first year.
C.
Collette's salary is $51,750 in her first year.
D.
After working at least one year at the company, Collette's salary is equal to last year's salary plus $1,035.
E.
After working at least one year at the company, Collette's salary is equal to last year's salary multiplied by 1.035.
F.
After working at least one year at the company, Collette's salary is equal to last year's salary multiplied by (n – 1).
Answers
GPT-4o mini
To determine which statements about Collette's salary are true, we need to analyze the provided statements along with the context of how her salary is calculated.
Let's break down the options:
A. **Collette's salary is $50,000 in her first year.**
- This cannot be verified without further information about the function mentioned, but generally, this could be a plausible first salary if established by the company's pay structure. Therefore, it might be true.
B. **Collette's salary is $51,035 in her first year.**
- Similar to statement A, this requires the specific function to verify. Therefore, this could also be a possibility but we cannot definitively say it's true without context.
C. **Collette's salary is $51,750 in her first year.**
- Again, without the specific function details, we cannot confirm this is true or false.
D. **After working at least one year at the company, Collette's salary is equal to last year's salary plus $1,035.**
- This statement suggests a fixed increment instead of a percentage increase. If the company's raise is purely cost-of-living based, it is unlikely that it's a fixed amount, hence this is likely false.
E. **After working at least one year at the company, Collette's salary is equal to last year's salary multiplied by 1.035.**
- This suggests that her salary is increasing by 3.5% each year, which is typically how cost-of-living adjustments work. Therefore, this statement is likely true.
F. **After working at least one year at the company, Collette's salary is equal to last year's salary multiplied by (n – 1).**
- This statement is incorrect; it implies that her salary would increase based on the number of years she's worked, but it should rather be an increase based on a percentage or fixed dollar amount relative to the last year's salary, rather than multiplying it by (n - 1).
Thus, based on our analysis without the specific salary function but inferring general salary increment practices, the most defensible statements would be:
- **A or B or C (one of these could potentially be true, but it depends on the salary function)**
- **E is likely true**
To summarize, the statements that could be true are A, B, C (depending on the salary function), and E is true. D and F appear to be incorrect based on the usual structure of annual salary increases.
Let's break down the options:
A. **Collette's salary is $50,000 in her first year.**
- This cannot be verified without further information about the function mentioned, but generally, this could be a plausible first salary if established by the company's pay structure. Therefore, it might be true.
B. **Collette's salary is $51,035 in her first year.**
- Similar to statement A, this requires the specific function to verify. Therefore, this could also be a possibility but we cannot definitively say it's true without context.
C. **Collette's salary is $51,750 in her first year.**
- Again, without the specific function details, we cannot confirm this is true or false.
D. **After working at least one year at the company, Collette's salary is equal to last year's salary plus $1,035.**
- This statement suggests a fixed increment instead of a percentage increase. If the company's raise is purely cost-of-living based, it is unlikely that it's a fixed amount, hence this is likely false.
E. **After working at least one year at the company, Collette's salary is equal to last year's salary multiplied by 1.035.**
- This suggests that her salary is increasing by 3.5% each year, which is typically how cost-of-living adjustments work. Therefore, this statement is likely true.
F. **After working at least one year at the company, Collette's salary is equal to last year's salary multiplied by (n – 1).**
- This statement is incorrect; it implies that her salary would increase based on the number of years she's worked, but it should rather be an increase based on a percentage or fixed dollar amount relative to the last year's salary, rather than multiplying it by (n - 1).
Thus, based on our analysis without the specific salary function but inferring general salary increment practices, the most defensible statements would be:
- **A or B or C (one of these could potentially be true, but it depends on the salary function)**
- **E is likely true**
To summarize, the statements that could be true are A, B, C (depending on the salary function), and E is true. D and F appear to be incorrect based on the usual structure of annual salary increases.