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

Let y denotes the salary in dollars and x denotes the time in hours.

$y = \begin{cases} 10 &\text{if } 0<x≤1 \\ 10 +1 0.2\lceil x-1 \rceil&\text{if } 1< x≤18 \end{cases}$ Graph of the function given below