A parking lot charges Rs 40 for the first 2 hours (or part thereof) and Rs 15 for…

MATHEMATICS · Single correct · AoPS · Mathematics · Special Functions · Special Functions

Problem

A parking lot charges Rs 40 for the first 2 hours (or part thereof) and Rs 15 for every additional hour (or part of an hour). Let

C(x)

denote the total charge (in rupees) for parking a car for

x

hours, where

x>0

. Which piecewise definition best represents

C(x)

? (a)

C(x)=\begin{cases}40x,&0<x\le 2\\15x,&x>2\end{cases}

(b)

C(x)=\begin{cases}40,&0<x<2\\40+15x,&x\ge 2\end{cases}

(c)

C(x)=\begin{cases}40,&0<x\le 2\\40+15(x-2),&x>2\end{cases}

(d)

C(x)=40+15x,\;x>0