In a certain country, the cost of sending a package by mail is a flat $25.00 up to the first 4 ounces. For each additional block of two ounces or less, the price increases by $0.20... In a certain country, the cost of sending a package by mail is a flat $25.00 up to the first 4 ounces. For each additional block of two ounces or less, the price increases by $0.20. Which graph below correctly represents this context?
Understand the Problem
The question is asking which graph correctly represents the cost structure for mailing a package, where the first 4 ounces costs a flat rate and subsequent blocks have incremental costs. The goal is to identify the graph that accurately depicts this information.
Answer
A
Answer for screen readers
The correct graph is A.
Steps to Solve
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Identify the Flat Rate for 4 Ounces
The cost for mailing up to the first 4 ounces is a flat rate of $25.00. This means that for any weight from 0 to 4 ounces, the cost remains constant. -
Determine Incremental Costs for Additional Weight
Beyond the first 4 ounces, the cost increases by $0.20 for every additional block of 2 ounces or less. Specifically:- From 4 ounces to 6 ounces: $25.20
- From 6 ounces to 8 ounces: $25.40
- From 8 ounces to 10 ounces: $25.60
- From 10 ounces to 12 ounces: $25.80
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Analyze Each Graph
We will examine which graph correctly shows a flat cost of $25.00 up to 4 ounces, and then increases by $0.20 for each additional weight block:- Graph A: Shows correct increments starting from 4 ounces.
- Graph B: Shows a flat line after the first 4 ounces, which is incorrect.
- Graph C: Displays an incorrect flat cost for weights above 4 ounces.
- Graph D: Incorrectly displays the cost increments.
The correct graph is A.
More Information
This problem illustrates the concept of piecewise functions, where the function's behavior changes based on the input value. Knowing how to interpret graphs and recognize patterns in costs will aid in various real-world applications.
Tips
- Ignoring the flat rate: Make sure to recognize that the cost does not change for weights between 0 and 4 ounces.
- Misreading increments: Ensure that the increases in cost are strictly according to the weight blocks defined (every 2 ounces).
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