Question

To send a standard letter through First-Class mail, the cost depends on the weight of the letter. Any letter one ounce or less will need $0.46 in postage. For each additional ounce over that, or any part of an ounce, the sender must add $0.20 more postage. Create a graph showing the cost of mailing standard First-Class letter weighing from 0 to one pound(16 ounces). Explain how you know your graph is correct.

Answer 1

Let x represents the total weight of the parcel and f(x) represents the cost of the parcel,

Then, according to the question,

Any letter one ounce or less will need $0.46 in postage.

That is, For 0 < x ≤ 1, f(x) = 0.46

For each additional ounce over that, or any part of an ounce, the sender must add $0.20 more postage,

Also, the maximum weight = 16 ounces,

0.46 + 0.20 (x-1)= 16

⇒ 0.20 (x-1) = 15.54

⇒ x-1 = 77.7⇒ x = 78.7

Hence, the function that shows the cost of the letter having weight greater than 1 ounces is,

And, for 1 < x ≤ 78.7 f(x) = 0.46 + 0.20(x-1),

Thus, the complete function that shows the given situation is,

`f(x) = \begin{Bmatrix}0.46, & 0\leq x\leq1\\ 0.46+0.20(x-1) & 1<x\leq78.7\end{Bmatrix}`

Thus, we get two line, y = 0.46 and y = 0.46 + 0.20(x-1),

Which are plotted in the below graph.