Question
\begin{tabular}{l} Use for questions \( 38-39 \) : Tabitha started working al a coflee shop making \( \$ 8.75 \) per hour. Every \\ six months, she gets a \( \$ 0.40 \) ralse. \\ \( \begin{array}{l}38 . \text { Write a formula to represent her hourly } \\ \text { wage after each raise. }\end{array} \) \\ \hline\end{tabular}
Ask by Riley Williams. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
Tabitha's hourly wage after each \$0.40 raise can be calculated using the formula:
\[
W(n) = 8.75 + 0.40n
\]
Where:
- \( W(n) \) is her hourly wage after \( n \) raises.
- \$8.75 is her starting wage.
- \$0.40 is the amount of each raise.
- \( n \) is the number of raises received.
For example, after 3 raises, her wage would be \$9.95 per hour.
Solution
To represent Tabitha's hourly wage after each \$0.40 raise every six months, you can use the following linear formula:
\[
W(n) = 8.75 + 0.40n
\]
**Where:**
- \( W(n) \) is Tabitha's hourly wage after \( n \) raises.
- \( 8.75 \) is her initial hourly wage in dollars.
- \( 0.40 \) represents the amount of each raise in dollars.
- \( n \) is the number of raises she has received.
**Example:**
If Tabitha has received 3 raises, her hourly wage would be:
\[
W(3) = 8.75 + 0.40 \times 3 = 8.75 + 1.20 = \$9.95 \text{ per hour}
\]
This formula allows you to calculate her wage at any point after consecutive raises.
Reviewed and approved by the UpStudy tutoring team
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Explain 
Simplify this solution Mind Expander
Let \( x \) represent the number of six-month periods that have passed since Tabitha started working. Her initial hourly wage is \( 8.75 \) and she receives a raise of \( 0.40 \) after each period. The formula to represent her hourly wage after \( x \) raises would be: \[ W(x) = 8.75 + 0.40x \] This formula allows you to calculate her wage at any point based on how long she's been working. Every six months she gets a raise, so after one year (which includes two raises), her wage would be: \[ W(2) = 8.75 + 0.40(2) = 8.75 + 0.80 = 9.55 \] Thus, in one year, she'd earn \( \$9.55 \) per hour! How exciting is that?
