Question

question 3 of 25
the equation $y = \

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

$ represents jordan’s overtime pay structure. based on this equation, after how many hours does jordan start earning overtime pay?

a. 30
b. 38
c. 25
d. 950

Explanation:

Step1: Analyze the piecewise function

The function is \( y=

$$\begin{cases}25x&0\leq x\leq38\\30(x - 38)+950&x>38\end{cases}$$

\). The first part (\(25x\)) applies for \(0\leq x\leq38\), and the second part (with a different rate, \(30\)) applies for \(x > 38\).

Step2: Identify overtime start

Overtime pay starts when the pay rate changes. The change in the function (from \(25x\) to \(30(x - 38)+950\)) occurs at \(x = 38\) (since for \(x>38\) the overtime - related formula is used). So Jordan starts earning overtime pay after 38 hours.

Answer:

B. 38