Question

your utility company charges 13 cents per kilowatt - hour of electricity. complete parts (a) and (b) below
a. what is the daily cost of keeping lit a 100 - watt light bulb for 13 hours each day?
b. how much will you save in a year if you replace the bulb with an led bulb that provides the same amount of light using only 20 watts of power?

a. the daily cost of keeping lit a 100 - watt light bulb for 13 hours each day is $0.169.
(round to three decimal places as needed.)
b. the yearly savings of replacing the 100 - watt light bulb with a 20 - watt light bulb is $\square.
(round to two decimal places as needed.)

Explanation:

Step1: Convert watt to kilowatt

Since \(1\) kilowatt \( = 1000\) watts, a \(100\) - watt bulb is \(100\div1000=0.1\) kilowatt and a \(20\) - watt bulb is \(20\div1000 = 0.02\) kilowatt.

Step2: Calculate daily energy consumption

For the \(100\) - watt (\(0.1\) kW) bulb, daily energy consumption \(E_1=0.1\times13 = 1.3\) kilowatt - hours. For the \(20\) - watt (\(0.02\) kW) bulb, daily energy consumption \(E_2=0.02\times13=0.26\) kilowatt - hours.

Step3: Calculate daily cost savings

The cost per kilowatt - hour is \(0.13\) dollars. Daily cost savings \(C_d=(E_1 - E_2)\times0.13=(1.3 - 0.26)\times0.13=1.04\times0.13 = 0.1352\) dollars.

Step4: Calculate yearly cost savings

Assume there are \(365\) days in a year. Yearly cost savings \(C_y=C_d\times365=0.1352\times365 = 49.348\approx49.35\) dollars.

Answer:

\(49.35\)