In Exercises 54 and 55 , your Internet service provider...

In Exercises 54 and 55 , your Internet service provider charges $\$ 4.95$ per month for the first 3 hours of service, plus $\$ 2.50$ for each additional hour. Your total charges last month were $\$ 21.83 .$ Let $x$ represent the number of hours you used the service. Which equation models the situation? A. $4.95+2.5 x-3=21.83$ B. $4.95+2.5(x-3)=21.83$

In Exercises 54 and 55 , your Internet service provider charges $\$ 4.95$ per month for the first 3 hours of service, plus $\$ 2.50$ for each additional hour. Your total charges last month were $\$ 21.83 .$ Let $x$ represent the number of hours you used the service.
Which equation models the situation?
A. $4.95+2.5 x-3=21.83$
B. $4.95+2.5(x-3)=21.83$

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Key Concepts

Fixed and Variable Costs

In cost models, fixed costs are those charges that do not change with usage, while variable costs change in proportion to the amount used. Recognizing which part of the cost is fixed and which part is variable is key to forming the correct algebraic expression for a given scenario.

Algebraic Modeling of Real-World Situations

Algebraic modeling involves translating a real-world scenario into an algebraic equation. This requires identifying constant values, rates, and thresholds accurately to construct an equation that precisely represents the scenario's pricing structure or any other relationship described.

Piecewise Functions

Piecewise functions are used to model situations where different rules apply to different parts of the domain. In many pricing problems, such as those with a limited free usage period followed by additional fees, the cost is determined by a basic rate for one segment and a different rule for any usage beyond that segment.

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