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In 2009 the U.S. Postal Service charged $1.17 postage for first-class mail retail flats (such as an 8.5 by 11 envelope) weighing up to 1 ounce,plus $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 relates C, the first-class postage charged, for a flat weighing x ounces.
Let me see.
I think all of this leads to a piecewise function.
The given information states:
1. For a flat weighing up to 1 ounce, the postage charged is $1.17.
2. For each additional ounce up to 13 ounces, an additional $0.17 is charged.
3. First-class rates do not apply to flats weighing more than 13 ounces.
Based on this information, we can create the following piecewise function:
C(x) = {$1.17, if 0 < x ≤ 1...top portion
C(x) = {$1.17 + $0.17(x - 1), if 1 < x ≤ 13...bottom portion
This was created by a math app.
Questions
1. C(x) represents the first-class postage charged for a flat weighing x ounces.
What information in the word problem indicates that I should define C(x) as states by the app?
2. Can you explain how to create the top and bottom portions of the piecewise function created by the math app?
3. The math app states that x represents the weight of the flat in ounces.
What information in the word problem makes this clear to us?
4. How would you break this type of problem step by step and as easy as possible to make sense for students?
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