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Most appliance manufacturers produce conventional and energy-efficient models. The energy- efficient models are more expensive to make but cheaper to operate. The costs of purchasing and operating a 36,000-Btu central air conditioner of each type are given in the Table. These costs do not include maintenance charges or changes in electricity prices.TableEnergy-Efficient ModelConventional ModelInitial Cost$4, 000$2, 700Capacity36, 000 Btu36, 000 BtuAnnual Cost of Electricity$932$1, 3321. Express the total cost Ce(x) and the average cost C ?e(x) = (1/x) Ce(x) of purchasing and operatingan energy-efficient model for x years.2. Express the total cost Cc(x) and the average cost C ?c(x) = 1/x Cc(x) of purchasing and operatinga conventional model for x years.3. Are the total costs for an energy-efficient model and for a conventional model ever the same? If so, when?4. Are the average costs for an energy-efficient model and for a conventional model ever the same? If so, when?

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average cost

energyefficient models

Annual Cost of Electricity

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