Chapter 2.4, Problem 59AYU

Wind Chill First-class Mail In 2015 the U.S. Postal Service charged $\$0.98$ postage for first-class mail retail flats (such as an $8.5"$ by $11"$ envelope) weighing up to 1 ounce, plus $\$0.22$ 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 relates $C$, the first-class postage charged, for a flat weighing $x$ ounces. Graph the function.

Source: United States Postal Service

To determine

To find:

a. Develop a model $C$, the first-class postage charged, for a flat weighing $x$ ounces.

Answer to Problem 59AYU

a. $\text{The function }f\text{can be defined as}$

$C\left(x\right) = \{\begin{array}{l}0.98 if x\le 1\\ 1.20 if 1<x\le 2\\ 1.42 if 2<x\le 3\\ 1.64 if 3<x\le 4\\ 1.86 if 4<x\le 5\\ 2.08 if 5<x\le 6\\ 2.30 if 6<x\le 7\\ 2.52 if 7<x\le 8\\ 2.74 if 8<x\le 9\\ 2.96 if 9<x\le 10\\ 3.18 if 10<x\le 11\\ 3.40 if 11<x\le 12\\ 3.62 if 12<x\le 13\end{array}$

Explanation of Solution

Given:

It is given that the U.S. Postal Service charged $\$0.98$ postage for first-class mail retail flats weighing up to 1 ounce, plus $\$0.22$ for each additional ounce up to 13 ounces.

a. Let the first-class postage charged, for a flat weighing $x$ ounces.

Upto 1 ounce, $\$0.98$.

1-2 ounce $0.98 + 0.22=\$1.2$

2-3 ounce $1.2 + 0.22=\$1.42$

3-4 ounce $1.42 + 0.22=\$1.64$

4-5 ounce $1.64 + 0.22=\$1.86$

5-6 ounce $1.86 + 0.22=\$2.08$

6-7 ounce $2.08 + 0.22=\$2.3$

7-8 ounce $2.3 + 0.22=\$2.52$

8-9 ounce $2.52 + 0.22=\$2.74$

9-10 ounce $2.74 + 0.22=\$2.96$

10-11 ounce $2.96 + 0.22=\$3.18$

11-12 ounce $3.18 + 0.22=\$3.4$

12-13 ounce $3.4 + 0.22=\$3.62$

First-class rates do not apply to flats weighing more than 13 ounces.

The function can be defined as,

$C\left(x\right) = \{\begin{array}{l}0.98 if x\le 1\\ 1.20 if 1<x\le 2\\ 1.42 if 2<x\le 3\\ 1.64 if 3<x\le 4\\ 1.86 if 4<x\le 5\\ 2.08 if 5<x\le 6\\ 2.30 if 6<x\le 7\\ 2.52 if 7<x\le 8\\ 2.74 if 8<x\le 9\\ 2.96 if 9<x\le 10\\ 3.18 if 10<x\le 11\\ 3.40 if 11<x\le 12\\ 3.62 if 12<x\le 13\end{array}$

To determine

To find:

b. Graph of the function $C$.

Answer to Problem 59AYU

b.

Explanation of Solution

Given:

It is given that the U.S. Postal Service charged $\$0.98$ postage for first-class mail retail flats weighing up to 1 ounce, plus $\$0.22$ for each additional ounce up to 13 ounces.

b.