Question

A local store owner pays her employees time-and-a-half for overtime. That means if an employee works more than 40 hours per week, the store will pay him 1.5 times his regular hourly wage of $6.50

Answer 1

Write and graph a piecewise function that illustrates an employee's weekly pay, W, as a function of the number of hours, h, that employee works.

Answer 2

having some trouble with this, if somebody could explain how i could solve this i would really appreciate it!

Answer 3

f(x) = 6.50x, x <=40
f(x) = 260 + 9.75x, x > 40

Sorry, that's the best I can do.

Answer 4

That's not really it, but it's close

Answer 5

thanks, i got this
does this seem to make sense or is this wrong?


P = {0 h<0
6.5 h 0≤h≤40
260+9.75 40<h≤168}

Answer 6

But you still need a variable for the the third interval.

Answer 7

The problem is, you need a variable that will represent h > 40 because it won't be the same as 0 < h < 40

Answer 8

for h > 40, it is overtime so it starts back at 1 again.

Answer 9

For instance, if she works one hour overtime, it won't be

260 + 9.75(41)

it will be
260 + 9.75(1)

For two hours, it will be
260 + 9.75(2)

so the variable cannot be h. It has to be "o" maybe for overtime hours.

But we have to write a piecewise function in terms of the same variable, so good luck with that.

Answer 10

I figured it out.

Answer 11

For the 3rd interval, you have to find the equation of the line. So use points


(40, 260) and (41, 269.75) to find the slope, then re-write the equation of the line in terms of h.

Answer 12

oh okay thank you soo much, what would the equation be in that case?

Answer 13

@Hero

Answer 14

wait

Answer 15

f(h) = 9.75h - 130

Answer 16

Tricky problem, but not impossible to figure out

Answer 17

so
f(h) = 6.50h 0 < h < 40
f(h) = 9.75h - 130 h > 40

Answer 18

@Hero thank you so much, i understand much better now. do you know how i could graph that?

Answer 19

never mind i got it :)