An electric company charges its customers S0.0577 per...

An electric company charges its customers S0.0577 per kilowatt-hour (kwh) for the first 1000 kWh used, 0.0532 dollar for the next $4000 \mathrm{kWh},$ and 0.0511 dollar for any kWh over 5000 . Find a piecewise-defined function $C$ for a customer's bill of $x$ kWh.

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Key Concepts

Piecewise Functions

A piecewise function is defined by different subfunctions, each applying to a certain interval of the domain. In the context of cost calculations, this method allows different pricing schemes or rates to be applied based on the consumption level or time period, providing a clear and organized way to model functions with varying behaviors over different segments.

Tiered Pricing

Tiered pricing is a strategy where the unit cost changes as the quantity consumed crosses certain thresholds. This model is commonly used in billing systems such as utilities where the first amount of consumption is charged at one rate, and subsequent consumption levels are charged at lower or higher rates, reflecting incentives or cost recoveries.

Cost Functions

A cost function represents the relationship between the quantity consumed and the total cost incurred. In this type of function, particularly in utility pricing, the cost function is often constructed in segments to accurately reflect the differing rates or costs that apply across various ranges of consumption.

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