Answer to Question #241391 in Calculus for Sid

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

$2. \text{The piecewise function can be given by }\\ f(x) = 10 \text{ if $0 < x \leq 1 $}\\ f(x) = \frac{2}{100}.10(x-1)+10 \text{ if 1$\leq x \leq 18$}\\ \implies f(x) = \begin{cases} 10 \text{ if 0 < x $\leq$ 1 }\\ \frac{2x+98}{10} \text{ if $1< x \leq 18$} \end{cases}\\$