A teacher's union has negotiated a uniform salary increase for each year of service up to 20 years. If a teacher started at $28,000 and 4 years later had a salary of 37,000, what function wpuld describe the teacher's salary over time?
S (n) is the teacher's salary over n years from the start of employment.
S (n)= _____
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To find the function that describes the teacher's salary over time, we can use the given information to determine the rate at which the salary increases each year.
The initial salary is given as $28,000, and 4 years later, the salary is $37,000. So, the increase in salary over the 4 years is $37,000 - $28,000 = $9,000.
Since the salary increase is the same for each year of service up to 20 years, the annual salary increase can be calculated as $9,000 / 4 = $2,250.
This means that each year, the salary increases by $2,250.
Now, we can write the function that describes the teacher's salary over time.
S(n) = $28,000 + $2,250n,
where S(n) is the teacher's salary over n years from the start of employment.
To find the function that describes the teacher's salary over time, we can analyze the given information.
We know that the teacher started with a salary of $28,000 and 4 years later had a salary of $37,000. We can assume that the salary increase is the same for each year of service.
To determine the annual increase, we can calculate the difference between the starting salary and the salary after 4 years: $37,000 - $28,000 = $9,000.
Since the increase is equal for each year, we can divide the total increase by the number of years, which is 4: $9,000 / 4 = $2,250.
Now, we can construct the function that describes the teacher's salary over time:
S(n) = Starting salary + (Annual increase × n)
Substituting the values we have:
S(n) = $28,000 + ($2,250 × n)
Therefore, the function that describes the teacher's salary over time is:
S(n) = $28,000 + ($2,250 × n)