Please Read the Question Below!

Question

An energy-efficient lightbulb, taking in 26.0 W of power, can produce the same level of brightness as a conventional lightbulb operating at power 100 W. The lifetime of the energy-efficient bulb is 10,000 h and its purchase price is $4.20, whereas the conventional bulb has lifetime 750 h and costs $0.54 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 $0.20 per kilowatt-hour.

$________

Answer 1

Cost = cost of bulbs + cost of the electricity

Let C₁ = cost of using the energy savings bulb and C₂ be the cost of using the conventional bulb.

26W = 26/1000 kW = 0.026 kW and the electricity used by an energy efficient bulb is 0.026(10,000) kW-hrs = 260 kW-hrs.

100W = 100/1000 kW = 0.1 kW and the electricity used by a conventional bulb is 0.1(10,000) kW-hrs = 1000 kW-hrs.

1 energy efficient bulb is required for 10,000 hrs

10000/750 = 13.333 = 14 conventional bulbs are required for 10,000 hrs.

C₁ = (cost of 1 bulb) + (cost of electricity) = 4.20 + 260(0.20) = $56.20

C₂ = (cost of 14 bulbs) + (cost of electricity) = 14(0.54) + 1000(0.20) = $207.56

Cost savings in using energy efficient bulbs (for 10,000 hrs) = $207.56 - $56.20 = $151.36