Question

A company that operates for 18 hours a day has introduced a new daily wage system that incorporates variable hourly rate to encourage longer shifts. The company pays $10 for first hour or any part of the first hour. Afterwards, company pays additional 2% per hour for each hour or part of each additional hour. Write a piece-wise function that shows the salary as a function of hours. Also sketch a graph of this function

Answer 1

Given : A company that operates for 18 hours a day has introduced a new daily wage system that incorporates variable hourly rate to encourage longer shifts.

The company pays $10 for first hour or any part of the first hour. Afterwards, company pays additional 2% per hour for each hour or part of each additional hour.

To Find :  Write a piece-wise function that shows the salary as a function of hours.

Also sketch a graph of this function

Solution:

The company pays $10 for first hour or any part of the first hour.

S(t)  salary function

t = number of hours worked

S(t)  = 10t   where  0 ≤ t ≤ 10

Afterwards, company pays additional 2% per hour for each hour or part of each additional hour.

Additional 2% = (2/100)10  = 0.2

Hence 10t + 0.2(t-10) = 10.2t-2  is paid

S(t)  = 10.2t - 2  where  10 < t  

Hence  a piece-wise function is :

$s(t)=\left \{ {{10t \quad 0 \leq t \leq 10} \atop {10.2t-2 \quad 10<t } } \right.$

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