Question

Terrance gets paid $10 an hour working at the Pizza Palace. Once he works over 40 hours he gets paid time and a half for up to 50 hours and he gets double time for all his time after that. Which expressions below can be used to create the piecewise-defined functions P(h) that defines Terrance's rates of pay?

Answer 1

Terrance's pay rate, P(h), is a piecewise-defined function representing $10/hour for the first 40 hours, time and a half for hours 41 to 50, and double time for hours beyond 50.

Step-by-step explanation:

Terrance's rate of pay can be defined by a piecewise-defined function, P(h), based on the number of hours worked, h. This function can be split into three parts:

• For the first 40 hours, he earns $10 per hour.
• For hours worked over 40 and up to 50 hours, he earns 'time and a half' which is $10 multiplied by 1.5.
• For hours worked beyond 50, he earns 'double time' which is $10 multiplied by 2.

Based on this information, the piecewise function P(h) can be represented as:

• If h ≤ 40, then P(h) = 10h
• If 40 < h ≤ 50, then P(h) = 10(40) + 15(h - 40)
• If h > 50, then P(h) = 10(40) + 15(10) + 20(h - 50)

The function reflects the standard pay for the first 40 hours, then includes the overtime pay at 1.5 times the regular rate for the next 10 hours, and finally calculates the double time pay for any hours over 50.