Answer to Question #241417 in Calculus for Phenominal1

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

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 :

$s(t)=\begin{cases} 10t\ \ \ 0\le t\le 10 \\ 10.2t-2\ \ \ 10<t \end{cases}$