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 $f(x)$ shows the total salary on hourly basis. $"x"$ denotes the number of hours.

$f(x) = \begin{cases} 10 &\text{if } x<=1 \\ (0.02+10)x &\text{if } 1<x<=18 \end{cases}$

Simplifying $f(x)$ , we get:

$f(x) = \begin{cases} 10 &\text{if } x<=1 \\ (10.02)x &\text{if } 1<x<=18 \end{cases}$

Graph of $f(x)$ will be: