OpenStax College Physics, Chapter 20, Problem 52 (Problems & Exercises)

This is College Physics Answers with Shaun Dychko. This question is asking how much should we be willing to pay for a fluorescent light bulb such that the total cost of operating it for a thousand hours would be the same as the total cost of operating an incandescent light bulb here? So the incandescent bulb has an upfront cost of 25 cents to buy it plus it consumes 60 watts of electricity and we'll turn that into kilowatts by multiplying by 1 kilowatt for every 1000 watts and then multiply by 1000 hours because that's the amount of time that we are told that it will operate for that's probably, you know, the expected lifetime of the bulb before it burns out and so we get kilowatt-hours here which we then multiply by 0.10 dollars per kW·h and the kilowatts and the hours both cancel and we are left with $6.25 is the total cost for the incandescent bulb that is the upfront cost plus the operating cost. So for the fluorescent bulb, we have some unknown upfront cost that we want to find plus the cost of operating it and the textbook has an example of 15 watts for a fluorescent bulb many bulbs are actually less wattage than this but let's assume this is what we have. So 15 watts times 1 kilowatt for every 1000 watts gives us kilowatts and then we multiply that by the number of hours—1000 hours— and then multiply by this rate for the electricity and we end up with some upfront cost x plus a $1.50 to operate it. So the total cost of the fluorescent is meant to equal the total cost of the incandescent bulb so that's x plus $1.5 of operating cost equals the total cost of the incandescent of $6.25. So we subtract a $1.50 from both sides and we end up with $4.75 would be the breakeven upfront cost that we would be willing to pay for the compact fluorescent. So considering only cost as a factor, if one was to see a bulb on sale for less than this then it would make financial sense to buy it.