Weekly Wage Function

[nycmathguy]

Section 1.6
Question 43

See attachments.

Part (a)

Evaluate top portion of function for W(30) & W(40).

Evaluate bottom portion of function for W(45) & W(50).

Yes?

See attachments for parts (b) and (c).

 

[MathLover1]

top portion of function is:

W(h)=14h

Evaluate:

W(30)
W(30)=14*30
W(30)=420
&
W(40) =14*40
W(40) =560

bottom portion of function is:

W(h)=21(h-40)+560

Evaluate:

W(45) =21(45-40)+560=665
&
W(50)=21(50-40)+560=770

 

[nycmathguy]

top portion of function is:

W(h)=14h

Evaluate:

W(30)
W(30)=14*30
W(30)=420
&
W(40) =14*40
W(40) =560

bottom portion of function is:

W(h)=21(h-40)+560

Evaluate:

W(45) =21(45-40)+560=665
&
W(50)=21(50-40)+560=770

In other words, I was right. What about parts (b) and (c)? Am I right about (b) and (c)?

 

[MathLover1]

(b) and (c) are correct

 

[nycmathguy]

(b) and (c) are correct

Wow! I took a wild guess for parts (b) and (c).

1. What does 21 represent?

2. What 560 represent?

 

[MathLover1]

1. What does 21 represent?
21 is pay per hour for overtime (21=14+0.5*14)

2. What 560 represent?
560 represents 40 hour wage (W(40) =560)

 

[nycmathguy]

1. What does 21 represent?
21 is pay per hour for overtime (21=14+0.5*14)

2. What 560 represent?
560 represents 40 hour wage (W(40) =560)

What is the difference between this textbook application and my salary thread posted earlier today?

 

[MathLover1]

What is the difference between this textbook application and my salary thread posted earlier today?

if you mean the difference between
W(h)=14h
W(h)=21(h-40)+560

and part b)
W(h)=16h=>the difference is in increase of hourly pay
W(h)=21(h-36)+560=>the difference is in regular work week decrease (to 36 hours)

and part c)

W(h)=16h=>the difference is in increase of hourly pay
W(h)=21(h-40)+560=>the regular work week is not changed (to 40 hours)

 

[nycmathguy]

if you mean the difference between
W(h)=14h
W(h)=21(h-40)+560

and part b)
W(h)=16h=>the difference is in increase of hourly pay
W(h)=21(h-36)+560=>the difference is in regular work week decrease (to 36 hours)

and part c)

W(h)=16h=>the difference is in increase of hourly pay
W(h)=21(h-40)+560=>the regular work week is not changed (to 40 hours)

Maybe a question will help clarify what I mean.

Question:

Can a piecewise function be formed to represent my salary situation for 40 hours at $16.50 per hour and $24.75 per hour in excess of 40 hours?

 

[MathLover1]

a piecewise function be formed to represent my salary situation for 40 hours at $16.50 per hour and $24.75 per hour in excess of 40 hours:

f(x)={ 16.50x if 0<x<=40
{ 24.75x if x>40

 

[nycmathguy]

a piecewise function be formed to represent my salary situation for 40 hours at $16.50 per hour and $24.75 per hour in excess of 40 hours:

f(x)={ 16.50x if 0<x<=40
{ 24.75x if x>40

Cool. This is what I was searching for. Piecewise functions are so mathematically intimidating. I like this fact about piecewise functions. Taking a break for a few days. We begin Section 1.7 aka Transformations of Functions in a few days.