Question

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

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

Answer 1

a) F (H) = 7H if H ≤ 40 hrs.

F (H) = 7H + 10.5 (EH) if H > 40 hrs i.e extra time.

b) P = 7 (40) + 10.5 (5) = 332.5$

Explanation:

a) In order to find piecewise function of pay rate, we need to understand how it is changing with conditions given.

Here, we are being told that, if a person works 40 hours, his/her wage per hour would be 7$ and if he/she exceeds this 40 hours time, it will count as over time or extra time and for that extra amount of time, he/she will be paid 1.5 times greater than normal. which is equal to 10.5$ per extra hour.

So, let's make the functions.

P = F (H) = 7H if H ≤ 40 hrs.

P = F (H) = 7H + 10.5 (EH) if H > 40 hrs i.e EH = extra hours.

b) for 45 hours it means there is 5 hours of Extra hours and 40 hours of normal time. Just plug in values in function number two for the condition if H > 40 hrs.

P = F (H) = 7H + 10.5 (EH)

P = 7 (40) + 10.5 (5)

P = 332.5$

Hope, this may help!