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#1 2021-06-10 19:40:10

nycmathguy
Member
Registered: 2021-06-02
Posts: 53

Find A Function

As of January 2013, the U.S. Postal Service
charged $0.92 postage for first-class retail flats (large envelopes)
weighing up to and including 1 ounce, plus a flat fee of $0.20 for
each additional or partial ounce up to and including 13 ounces.
First-class rates do not apply to flats weighing more than
13 ounces.

Find a function C that models the first-class postage charged,
in dollars, for a large envelope weighing w ounces. Assume
w > 0.

I have been struggling with questions requiring a function to be constructed from written information. I believe that this is one of the most important techniques to develop in mathematics. In fact, sometimes I feel like concentrating on this skill above the rest.

The question posted here is number 60 (an even number question). There are no answers in the back of the book for even number questions.  So, I decided to use the answer to question 59 as a guide to make the function given below. Otherwise, I could not even begin to write the information as shown that may or may not be right.

Let c(w) be a piecewise function.

I think this is a four-part piecewise function based on the answer for question 59.

Let c(w) equal the following:

0.92     0 < w ≤ 1
1.12     1 < w ≤ 2
1.32     2 < w ≤ 3
1.52     3 < w ≤ 13

Is this right?

Last edited by nycmathguy (2021-06-10 19:48:16)

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#2 2021-06-12 19:17:47

Bob
Administrator
Registered: 2010-06-20
Posts: 9,228

Re: Find A Function

hi nycmathguy

Just discovered this post. 
Surely the cost goes up for each step up in w. 

I've got a 13 line function definition covering (0,1], (1,2], (2,3] ...(12,13] where an open bracket means don't include the endpoint and a square bracket means do include it. And then over 13 a statement that the function is undefined.

But it would be good practice for you to try and  and express lines two up to thirteen in a single expression using a suitable step definition.  The choices are floor, in which the charge is truncated down to the first lower integer, and ceiling in which the charge is rounded up.

Decide which of these two is the correct one and also find a suitable algebraic expression for the charge applicable.  You need to include the fixed charge for the first oz, and then the m value to reflect how the charge increases for each subsequent oz added.

In another reply I gave you a link to mathword where these two functions are illustrated.  The MIF function plotter will handle floor and ceiling so you can test your function by making a graph.

Bob


Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob smile

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#3 2021-06-13 08:25:29

nycmathguy
Member
Registered: 2021-06-02
Posts: 53

Re: Find A Function

Bob wrote:

hi nycmathguy

Just discovered this post. 
Surely the cost goes up for each step up in w. 

I've got a 13 line function definition covering (0,1], (1,2], (2,3] ...(12,13] where an open bracket means don't include the endpoint and a square bracket means do include it. And then over 13 a statement that the function is undefined.

But it would be good practice for you to try and  and express lines two up to thirteen in a single expression using a suitable step definition.  The choices are floor, in which the charge is truncated down to the first lower integer, and ceiling in which the charge is rounded up.

Decide which of these two is the correct one and also find a suitable algebraic expression for the charge applicable.  You need to include the fixed charge for the first oz, and then the m value to reflect how the charge increases for each subsequent oz added.

In another reply I gave you a link to mathword where these two functions are illustrated.  The MIF function plotter will handle floor and ceiling so you can test your function by making a graph.

Bob

I will play with this problem some more.

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