Question

You have a summer job that pays time and a half for overtime. That is, if you work more than 40 hours per week, your hourly wage for the extra hours is 1.5 times your normal hourly wage of $7.

Write a piecewise function that gives your weekly pay P in terms of the number h of hours you work. How much will you get paid if you work 45 hours?

A) $368.5
B) $332.5
C) $452.5
D) None of these

Answer 1

To write a piecewise function for weekly pay, use $7 for up to 40 hours and time and a half for extra hours. If you work 45 hours, you will get paid $332.50.

Step-by-step explanation:

To write a piecewise function for your weekly pay, you need to consider two scenarios: working less than or equal to 40 hours and working more than 40 hours.

If you work 40 hours or less, your weekly pay will be the number of hours worked multiplied by your hourly wage, which is $7: P(h) = 7h.

If you work more than 40 hours, your weekly pay will be the sum of two parts: the pay for the first 40 hours, which is 40 multiplied by $7, and the pay for the extra hours, which is (h - 40) multiplied by 1.5 times your hourly wage: P(h) = 7(40) + 1.5(7)(h - 40).

To find out how much you will get paid for working 45 hours, substitute h = 45 into the piecewise function: P(45) = 7(40) + 1.5(7)(45 - 40) = 280 + 1.5(7)(5) = 280 + 1.5(35) = 280 + 52.5 = $332.50.