Your weekly hours are based on weather conditions. You earn $30 per hour for up to 40 hours and you are limited to at most 10 hours of overtime at one and one-half times your base pay rate.

Question

a. Write and graph a piecewise defined function E(x) that gives your earnings E for working x hours in one week. Are your earnings ever directly proportional to the number of hours you work? Explain.

b. Find your weekly earnings when you work 35 hours and when you work 50 hours.

c. Find and interpret the slope of each segment of the graph of E(x).

d. Find and interpret the intercepts of the graph of F(x).

e. You earn $1515 in one week. How many hours did you work? ​

Answer 1

E(x) = 1200 +45(x-40) for 40<x< 50

E(x) = 45x -600, for 40<x<50

E(x) = 30x if x<40

Earnings are proportional to hours worked, if x < 40 hours

E(35) = 30(35) = $1050 for 35 hours

E(50) = 30(40)+45(10) = 1200+450 = $1650 for 50 hours

for 0<x<40 the slope =30 = the hourly wage for regular time

for 40<x<50 the slope = 45 = hourly wage for overtime

y intercept for E(x) = 0. work zero hours, you get paid $0

1515 = 45x-600

45x = 2115

x = 2115/45 = 47 hours worked to get $1515