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). a. complete the table to help find an equation for t and s. show the arithmetic that helps to identify the pattern. (do not include the $ symbol in your answers.) time at company (years) t salary (thousands of dollars) s 0 (2·□) + □ 1 (2·□) + □ 2 (2·□) + □ 3 (2·□) + □ 4 (2·□) + □ s = □ (type an expression using t as the variable.)

Explanation:

Step1: Analyze t=0

At \( t = 0 \) (starting year), the salary \( s \) is 16 (thousand dollars). The formula given is \( (2 \cdot \square)+ \square \). For \( t = 0 \), \( 2 \cdot 0+16 = 16 \), so the first blank is 0 and the second is 16.

Step2: Analyze t=1

At \( t = 1 \), the salary is starting salary plus raise: \( 16 + 2=18 \). Using the formula \( (2 \cdot 1)+16 = 2 + 16=18 \), so first blank 1, second 16.

Step3: Analyze t=2

At \( t = 2 \), salary is \( 16+2\times2 = 20 \). Formula: \( (2 \cdot 2)+16 = 4 + 16 = 20 \), first blank 2, second 16.

Step4: Analyze t=3

At \( t = 3 \), salary is \( 16+2\times3 = 22 \). Formula: \( (2 \cdot 3)+16 = 6 + 16 = 22 \), first blank 3, second 16.

Step5: Analyze t=4

At \( t = 4 \), salary is \( 16+2\times4 = 24 \). Formula: \( (2 \cdot 4)+16 = 8 + 16 = 24 \), first blank 4, second 16.

Step6: Find general equation

The pattern is that for time \( t \) years, the salary \( s \) (in thousands) is \( 2t + 16 \), since each year \( t \) we add \( 2t \) (raise per year times years) to the starting salary 16.

Filling the table:

• \( t = 0 \): \( (2 \cdot 0)+16 \)
• \( t = 1 \): \( (2 \cdot 1)+16 \)
• \( t = 2 \): \( (2 \cdot 2)+16 \)
• \( t = 3 \): \( (2 \cdot 3)+16 \)
• \( t = 4 \): \( (2 \cdot 4)+16 \)

And the equation for \( s \) is \( s = 2t + 16 \)

Answer:

For the table blanks (from top row to bottom row for each t):

• t=0: 0, 16
• t=1: 1, 16
• t=2: 2, 16
• t=3: 3, 16
• t=4: 4, 16

And \( s=\boxed{2t + 16} \)