Question

The 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 a person work h hours for the company

Note if $0<h\le 1$ then the company pays $10

If $1<h\le2$ then the company pays $$10+10+\frac{2*10}{100}$

If $2<h\le 3$ then the company pays $$10+10+10+\frac{2*(3-1)*10}{100}$

=$30+\frac{2*(3-1)*10}{100}$

So for h hours the company pays $10*h+\frac{2*(h-1)*10}{100}$ ,h>0

So the function is;

$\begin{cases} 10 &\text{if } 0<h\le1 \\ 10+10+\frac{1}{5} &\text{if } 1<h\le 2 \\ 10+10+10+\frac{2}{5} &\text{if } 2<h\le 3 \\10+10+10+10+\frac{3}{5} &\text{if }3<h\le 4 \end{cases}$

The graph is as below,