An energy-efficient lightbulb, taking in 25.0 W of power, can produce the same level of brightness as a conventional bulb operating at power 100 W. The lifetime of the energy-efficient bulb is 10,000 h and its purchase price is $17.00, whereas the conventional bulb has lifetime 750 h and costs $0.420 per bulb. Determine the total savings obtained by using one energy-efficient bulb over its lifetime as opposed to using conventional bulbs over the same time period. Assume an energy cost of $0.0870 per kilowatt-hour.

Question

An energy-efficient lightbulb, taking in 25.0 W of power, can produce the same level of brightness as a conventional bulb operating at power 100 W. The lifetime of the energy-efficient bulb is 10,000 h and its purchase price is $17.00, whereas the conventional bulb has lifetime 750 h and costs $0.420 per bulb. Determine the total savings obtained by using one energy-efficient bulb over its lifetime as opposed to using conventional bulbs over the same time period. Assume an energy cost of $0.0870 per kilowatt-hour.
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Henry · Answer

Energy-efficient bulb:

Cost = $17.00 + $0.0870/kwh * (0.025kw * 10,000h) = $38.75.

Conventional Bulb:

# of bulbs = 10000h * (1/750)bulbs/h =
13.3333Bulbs.

Cost = 13.3333bulbs * 0.42/bulb + $0.0870/kwh * (0.10kw * 10,000h) = $92.60.

Savings = 92.60 - 38.75 = $53.85..