Question

Electricity rates An electric company charges its customers $\$ 0.0577$ per kilowatt-hour (kWh) for the first 1000 kWh used, $\$ 0.0532$ for the next 4000 kWh, and $\$ 0.0511$ for any kWh over $5000 .$ Find a piecewise-defined function $C$ for a customer's bill of $x \mathrm{kWh}$

Name: Problem 70, Chapter 2: Precalculus: Functions and Graphs
Uploaded: 2021-05-17T21:13:28-08:00
Duration: 2 min 17 s
Channel: Benjamin Chaback
Description: Electricity rates An electric company charges its customers 0.0577 per kilowatt-hour (kWh) for the first 1000 kWh used, 0.0532 for the next 4000 kWh, and 0.0511 for any kWh over 5000 . Find a piecewise-defined function C for a customer's bill of x kWh

   Electricity rates An electric company charges its customers $\$ 0.0577$ per kilowatt-hour (kWh) for the first 1000 kWh used, $\$ 0.0532$ for the next 4000 kWh, and $\$ 0.0511$ for any kWh over $5000 .$ Find a piecewise-defined function $C$ for a customer's bill of $x \mathrm{kWh}$

Precalculus: Functions and Graphs

Earl W. Swokowski,… 12th Edition

Chapter 2, Problem 70

Instant Answer

Solved by Expert Benjamin Chaback

05/17/2021

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The company charges its customers $\$0.0577$ per kilowatt-hour (kWh) for the first 1000 kWh used, $\$0.0532$ for the next 4000 kWh, and $\$0.0511$ for any kWh over 5000. Show more…

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Electricity rates An electric company charges its customers $\$ 0.0577$ per kilowatt-hour (kWh) for the first 1000 kWh used, $\$ 0.0532$ for the next 4000 kWh, and $\$ 0.0511$ for any kWh over $5000 .$ Find a piecewise-defined function $C$ for a customer's bill of $x \mathrm{kWh}$

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Key Concepts

Piecewise Functions

A piecewise function is defined by different expressions over different intervals of the domain. This is particularly useful when modeling situations where the behavior changes based on conditions or thresholds, such as varying electricity rates based on usage amounts.

Tiered Pricing

Tiered pricing involves applying different rates for different levels or ‘tiers’ of consumption. In contexts like utility billing, customers are charged at a higher rate for initial usage and a lower rate as usage increases, which encourages conservation and reflects the cost structure of service provision.

Cost Calculation Methods

Cost calculation in a tiered pricing model involves determining the cost by multiplying the usage in each tier by the corresponding rate, then summing these costs. This method requires careful segmentation of the total consumption across the defined usage intervals to accurately compute the overall charge.

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