To determine Michelle's overtime hourly pay from the given piecewise function [tex]\( y \)[/tex], let's break down the equation in detail.
The function is defined as:
[tex]\[ y = \begin{cases}
25x & \text{for } 0 \leq x \leq 38 \\
30(x - 38) + 950 & \text{for } x > 38
\end{cases} \][/tex]
1. Regular Wage:
- For [tex]\( 0 \leq x \leq 38 \)[/tex], the equation is [tex]\( y = 25x \)[/tex].
- Here, [tex]\( x \)[/tex] represents the number of hours worked.
- The coefficient 25 is Michelle's hourly wage for regular hours.
2. Overtime Wage:
- For [tex]\( x > 38 \)[/tex], the equation is [tex]\( y = 30(x - 38) + 950 \)[/tex].
- [tex]\( x - 38 \)[/tex] represents the number of overtime hours worked beyond 38 hours.
- The coefficient 30 indicates the increase in wages for each hour worked overtime.
- The constant term 950 is the total wage received for the 38 regular hours, calculated as [tex]\( 25 \times 38 \)[/tex].
Through this breakdown, we can clearly see that:
- Michelle's regular hourly wage is [tex]\( 25 \)[/tex] dollars per hour.
- Michelle's overtime hourly pay is [tex]\( 30 \)[/tex] dollars per hour for any hour worked beyond 38 hours.
Thus, Michelle's overtime hourly pay is [tex]\( 30 \)[/tex] dollars per hour.
