Question

Assume it costs 30 cents to mail a letter weighing one ounce or less, and then 28 cents for each additional ounce or fraction of an ounce. Write a piecewise-defined function P(x) that represents the cost, in cents, of mailing a letter weighing between 0 and 3 ounces.

Answer 1

`P(x) = 30, 0\leq x \leq 1\\~~~~~~~=58, 1 < x \leq 2\\~~~~~~~=86,2<x \leq 3`

Explanation:

We are given the following in the question:

Cost of sending a mail =

30 cents for 1 ounce or less.

28 cents for each additional ounce or fraction of an ounce.

Let x represent the weight of mail. Let P(x) represents the cost in cents.

Weight of mail between 0 and 1 ounces

`P(x) =30\text{ cents}, 0\leq x \leq 1`

Weight of mail between 1 and 2 ounces

`P(x) =(30 + 28)\text{ cents}\\P(x) =(58)\text{ cents}, 1 < x \leq 2`

Weight of mail between 2 and 3 ounces

`P(x) =(58 + 28)\text{ cents}\\P(x) =(86)\text{ cents}, 2 < x \leq 3`

Thus, we can write the piecewise function for cost in the following manner:

`P(x) = 30, 0\leq x \leq 1\\~~~~~~~=58, 1 < x \leq 2\\~~~~~~~=86,2<x \leq 3`

where x is in ounces and P(x) is the cost in cents.