Question

question 8 of 10
the equation $y = \

$$\begin{cases} 25x & 0 \\leq x \\leq 38 \\\\ 30(x - 38) + 950 & x > 38 \\end{cases}$$

$ represents michelles regular hourly and overtime wage. based on this equation, after how many hours worked does michelle start earning overtime pay?
\\( \bigcirc \\) a. 30
\\( \bigcirc \\) b. 38
\\( \bigcirc \\) c. 950
\\( \bigcirc \\) d. 25

Explanation:

Step1: Analyze the piecewise function

The function is defined as \( y =

$$\begin{cases} 25x & 0 \leq x \leq 38 \\ 30(x - 38)+950 & x > 38 \end{cases}$$

\). The first part (\(25x\)) is for regular hours, and the second part is for overtime.

Step2: Identify the overtime start

Overtime starts when the function switches from the regular wage formula to the overtime formula. This happens at the boundary of the intervals. The regular hours interval is \(0 \leq x \leq 38\), and overtime is for \(x > 38\). So the start of overtime is at \(x = 38\) hours.

Answer:

B. 38