Question

To package and ship an item, it costs $6.25 for the first pound and $1.35 for each additional pound. Write an explicit rule, find the 13th term, and explain what it represents.

Answer 1

An explicit rule for the shipment cost is C(n) = 6.25 + 1.35(n - 1), where n ≥ 1. Plugging in 13 for n, we find the cost for a 13-pound item to be $22.45. This cost represents the total price to ship an item that weighs 13 pounds.

Step-by-step explanation:

The question asks us to create an explicit rule for calculating the cost of shipping an item based on its weight, identify the cost of shipping a 13-pound item, and explain the meaning of this value. To find the explicit rule, we consider the fact that it costs $6.25 to ship the first pound and $1.35 for each additional pound. This situation is a linear function, where the independent variable is the weight of the item in pounds (n), and the dependent variable is the total cost (C).

The explicit rule can be written as follows:
C(n) = 6.25 + 1.35(n - 1), where n ≥ 1.

To find the 13th term, we substitute n with 13:
C(13) = 6.25 + 1.35(13 - 1) = 6.25 + 1.35(12) = 6.25 + 16.20 = 22.45.

The 13th term, which is $22.45, represents the cost to ship an item that weighs 13 pounds.