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).
1 | (2·1) + 16
2 | (2·2) + 16
3 | (2·3) + 16
4 | (2·4) + 16
s = 2t + 16 (type an expression using t as the variable.)
b. perform a unit analysis of the equation found in part (a). choose the correct answer.
a. the units of the expressions on both sides of the equation are dollars.
b. the units on the left side of the equation are thousands of dollars and the units on the right side of the equation are years.
c. the units of the expressions on both sides of the equation are years.
d. the units on the left side of the equation are years and the units on the right side of the equation are thousands of dollars.

Explanation:

To analyze the units: The left - hand side (LHS) \(s\) is defined as salary in thousands of dollars. For the right - hand side (RHS): The term \(2t\): the raise is \(\$2\) thousand per year, so the unit of \(2\) is thousands of dollars per year, and \(t\) is in years. When we multiply \(2\) (thousands of dollars/year) by \(t\) (years), the “year” units cancel out, and we get thousands of dollars. The term \(16\) is the starting salary in thousands of dollars. So when we add \(2t\) (thousands of dollars) and \(16\) (thousands of dollars), we get a result in thousands of dollars, which matches the unit of \(s\) (thousands of dollars). Let's check the options:

• Option A: The units are not dollars (they are thousands of dollars), so A is incorrect.
• Option B: The RHS units are not years (they are thousands of dollars), so B is incorrect.
• Option C: The units are not years, so C is incorrect.
• Option D: The LHS unit is thousands of dollars (not years) and the RHS unit is thousands of dollars, so D is incorrect. Wait, there is a mistake in the above analysis. Wait, the problem says \(s\) is salary in thousands of dollars. The coefficient of \(t\) is \(2\) (thousands of dollars per year), \(t\) is in years. So \(2t\) has units (thousands of dollars/year)\(\times\)year = thousands of dollars. The constant term \(16\) is in thousands of dollars. So both sides have units of thousands of dollars. But looking at the options again, maybe the problem considers "thousands of dollars" as a unit related to dollars. Wait, maybe the question has a wording issue, but among the options, the only one that makes sense in terms of unit consistency is that both sides have the same unit (related to dollars). Option A says "dollars" (maybe it's a simplification, considering "thousands of dollars" as a multiple of dollars). Let's re - evaluate:

The left side \(s\) is salary in thousands of dollars. The right side: \(2\) (thousand dollars per year) \(\times t\) (years) gives thousand dollars, and \(16\) is thousand dollars. So when we consider the actual dollar amount, if we think of \(s\) as representing a dollar amount (with the understanding that the number is in thousands), then both sides are in dollars. For example, if \(t = 1\), \(s=2(1)+16 = 18\) (thousand dollars) or \(18000\) dollars. So the units of both sides, when considered as dollar amounts (with the coefficient accounting for thousands), are dollars. So Option A is correct.

Answer:

A. The units of the expressions on both sides of the equation are dollars.