The cost of mailing a package weighing up to, but not...

The cost of mailing a package weighing up to, but not including, 1 pound is 2.72 dollars. Each additional pound or portion of a pound costs 0.50 dollars. (a) Use the greatest integer function to create a model for the cost $C$ of mailing a package weighing $x$ pounds, where $x>0$ (b) Sketch the graph of the function.

The cost of mailing a package weighing up to, but not including, 1 pound is 2.72 dollars. Each additional pound or portion of a pound costs 0.50 dollars.
(a) Use the greatest integer function to create a model for the cost $C$ of mailing a package weighing $x$ pounds, where $x>0$
(b) Sketch the graph of the function.

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Greatest Integer Function

This function, also known as the floor function, takes a real number as input and returns the largest integer that is less than or equal to that number. It is useful in modeling scenarios where values are rounded down to an integer, which can be crucial when determining cost increments or units in a stepwise manner.

Step Functions

Step functions are those that have constant values on intervals but jump to different values at certain points. They are ideal for representing situations in real-life applications—such as pricing schemes—where a fixed charge applies for each complete or partial unit, resulting in abrupt changes in cost rather than a continuous variation.

Mathematical Modeling of Real-World Pricing

This concept involves creating a mathematical function that represents a real-world pricing structure. It requires identifying the base cost and additional incremental costs, and then appropriately using functions like the greatest integer function to account for the 'per unit or fraction thereof' condition. Such models help in accurately calculating costs as the input variable (for example, weight) changes.

Transcript

Please give Ace some feedback