March 29, 2017

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You can buy an energy-saving light bulb for $18.07, which can work for 10,000 hours. It costs you 0.8 cents to operate it for an hour. ($1=100 cents). A regular light bulb with the same intensity costs 39 cents. The light bulb can work for 1000 hours. It costs you 3.4 cents to operate it for an hour. After how many hours of operation is the energy-saving light bulb more economical?

Thank You!

  • Math - ,

    Bulb A total cost (including depreciation) = 18.07 t/10,000 + 0.008 t
    = 0.02607 per hour
    Bulb B total cost (including depreciation) = 0.39 t/1000 + .034 t
    = 0.03439 per hour

    A is always less expensive, in the long run, when bulb replacement costs are included. But they probably want you to know "How soon before you save enough to pay for the energy-saving bulb?". For that answer, solve this equation:

    18.07 + 0.008 t = 0.39 + .034 t
    17.68 = 0.026 t
    t = 680 hours, before the lamp B burns out

    Nowadays, compact fluorescent energy-saving bulbs cost quite a bit less than 18.07, and the savings come much sooner.

  • Math - ,

    Thank you very much! Great answer!

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