Q. 59 - Precalculus Enhanced with Graphing Utilities

Question

In 2011 the U.S. Postal Service charged $\backslash (0.88$ postage for first-class mail retail flats (such as an $8.5\text{'}\text{'}$ by $11\text{'}\text{'}$ envelope) weighing up to $1$ ounce, plus $\backslash )0.17$ for each additional ounce up to $13$ ounces. First-class rates do not apply to flats weighing more than $13$ ounces. Develop a model that related C, the first-class postage charged, for a flat weighing x ounces. Graph the function.

Step-by-Step Solution

Answer

The required model is $C=\left\{\begin{array}{ll}0.71+0.17x for& x>1\\ 0.88 for& x<1\end{array}\right.$.

On plotting the function, we get,

Step 1. Given information.

Consider the given question,

Postal charge for first-class mail weighing upto $1$ ounces is $\$0.88$.

Postal charge for first-class mail for additional ounces upto $13$ ounces is $\$0.17$for each additional ounce. Then,

$=0.17\left(x-1\right)$

When $x>1$ postal charge for first-class mail flats for x ounces is $0.71+0.17x$.

When $x<1$ the postal charge for first-class mail retail flats for x ounces is $\$0.88$.

Hence, we can say the C models, for weighing x ounces is given below,

$C=\left\{\begin{array}{ll}0.71+0.17x for& x>1\\ 0.88 for& x<1\end{array}\right.$

Step 2. Plot the graph.

On plotting the graph,