Question

a person earns a starting salary of $16 thousand at a company. each year, she receives a $2 thousand raise. let s be the salary (in thousands of dollars) after she has worked at the company for t years. complete parts (a) through (e).
d. what is the s-intercept? what does it mean in this situation?
select the correct choice and fill in the answer box to complete your choice.
(type an ordered pair.)
a. the s-intercept of the model is , and it represents the persons salary when she quits the job.
b. the s-intercept of the model is (0,16), and it represents the persons salary when she joined the company.
e. when will the person’s salary be $30 thousand?
the persons salary will be $30 thousand after \\(\square\\) years.
(type an integer or a decimal.)

Explanation:

Step1: Determine the salary function

The salary \( s \) (in thousands of dollars) after \( t \) years can be modeled by a linear equation. The starting salary (when \( t = 0 \)) is 16 thousand dollars, and the annual raise is 2 thousand dollars. So the equation is \( s = 2t + 16 \).

Step2: Solve for \( t \) when \( s = 30 \)

We set \( s = 30 \) in the equation \( 30 = 2t + 16 \).
Subtract 16 from both sides: \( 30 - 16 = 2t \), which simplifies to \( 14 = 2t \).
Divide both sides by 2: \( t=\frac{14}{2}=7 \).

Answer:

7