Question

In 2012, first class letter postage was $0.45 for up to one ounce and $0.20 each additional ounce or part of an ounce. Which step function models this scenario where x represents weight of the letter in ounces? A

Answer 1

To model the postage costs as a function of letter weight in 2012, a step function is used where the cost is $0.45 for up to one ounce and increases by $0.20 for each additional ounce. The total cost is calculated by adding $0.20 for every ounce above the first, applying the ceiling function to account for any part of an ounce.

Step-by-step explanation:

The question relates to the modeling of postage costs as a function of the weight of a letter using a step function. Since the cost is $0.45 for the first ounce in 2012 and $0.20 for each additional ounce or part, the step function would increase by $0.20 at each ounce mark past the first ounce. For a letter weighing x ounces, the cost C(x) in dollars could be defined as:

C(x) = 0.45 for 0 < x ≤ 1

C(x) = 0.45 + ∈⁴(x - 1) × 0.20 for x > 1, where ∈⁴ is the ceiling function, which rounds x up to the nearest integer.

This step function represents the total postage cost, where each step signifies an increase in weight and corresponding increase in cost. This function is appropriate for calculating postage for a given letter's weight.