Question

A leasing agent makes $23 an hour for the first 40 hours he works during a week and $30 an hour for each hour over 40 hours. Which piece wise equation models his total weekly pay y in dollars as it relates to the number of hours x that he has worked during this week?

Answer 1

f(x)= { 23x, 0<x<=40

2120-30x, x>40 }

Explanation:

A leasing agent makes $23 an hour for the first 40 hours he works during a week and $30 an hour for each hour over 40 hours.

In piecewise function , we write two functions

one for first 40 hours and another for more than 40 hours

A leasing agent makes $23 an hour for the first 40 hours he works during a week . LEt x be the number of hours worked

So f(x)= 23x, 0<x<=40

$30 an hour for each hour over 40 hours.

40-x represents the hours more than 40. we need total weekly pay. so we add the weely pay for 40 hours as well

f(x)= 30(40-x) +23*40, x>40

f(x)= 1200-30x+920, x>40

f(x)= 2120-30x, x>40

Now we write piecesise funtion

f(x)= { 23x, 0<x<=40

2120-30x, x>40 }

Answer 2

For this case we have:

Let x the number of hours the leasing agent works for a week.

Case 1:

If the leasing agent works 40 hours we have the following function that represents your weekly payment in dollars:

`f (x) = 23x\ when \ 0 <x\leq 40`

Case 2:

If the leasing agent works more than 40 hours, every hour after 40 is paid at $ 30. In this case the weekly payment in dollars is given by the following function:

`f (x) = 30 (x-40) + (23 * 40)\ when \ x> 40`

Thus, the weekly payment of the leasing agent is given by the following function:

`f(x)=\left \{ {{23x\ when\ 0 <x\leq 40} \atop {30 (x-40) + (23 * 40)\ when\ x> 40}} \right.`

Answer:

`f(x)=\left \{ {{23x\ when\ 0 <x\leq 40} \atop {30 (x-40) + (23 * 40)\ when\ x> 40}} \right.`