Q50.

Question

Answer the question that was passed at the beginning of the lesson.

How do step functions apply to postage rates?

Include the following in your answer:

  • An explanation of why a step function is the best model for this situation, while your gas mileage as a function of time as you drive to the post office cannot be modeled with a step function, and 
  • A graph of a function that represents the cost of a first- class letter.

Step-by-Step Solution

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Answer

The graph of the function is shown below:


1Step-1 – Step function.

The graph of a step function is not linear. It consists of line segments or rays.

2Step-2 – Determine the function.

A step function can be used to model the cost of a letter in terms of its weight.

Given:

Here, weight of the letter is x.

Total postage cost is y.

The gas mileage of a car be any real number in an interval of real numbers, so it cannot be modeled by a step function. Gas mileage is a continuous function of time.

3Step-3 – Graph for function.

The graph of the function is shown below: