Question

a shipping company charges $6 to ship a package that weighs up to 1 pound and $2 for each additional pound or portion of a pound. which equation represents the cost, in dollars, of shipping a package that weighs x pounds?
○ $f(x) = 6 + 2\lceil x - 1 \
ceil$, where $x > 0$
○ $f(x) = 6 + 2\lfloor x - 1 \
floor$, where $x > 0$
○ $f(x) = 6 + 2\lceil x + 1 \
ceil$, where $x > 0$
○ $f(x) = 6 + 2\lfloor x + 1 \
floor$, where $x > 0$

Explanation:

Step1: Understand the cost structure

Base cost: $\$6$ for $0 < x \leq 1$. For $x>1$, add $\$2$ per extra pound/portion.

Step2: Identify the floor/ceiling need

We need to count every portion of a pound as a full pound. For $x>1$, the number of extra pounds/portions is given by the ceiling of $(x-1)$, written as $\lceil x-1
ceil$.

Step3: Build the cost function

Total cost = base cost + 2 * number of extra portions: $f(x)=6+2\lceil x-1
ceil$ for $x>0$.

Step4: Match to options

This matches the first option.

Answer:

A. $f(x)=6+2\lceil x-1
ceil$, where $x>0$