Question

your utility company charges 14 cents per kilowatt - hour of electricity. complete parts (a) and (b) below.
a. what is the daily cost of keeping lit a 50 - watt light bulb for 11 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 50 - watt light bulb for 11 hours each day is $\square$. (round to three decimal places as needed.)

Explanation:

Step1: Convert watts to kilowatts

The power of the light - bulb is 50 watts. Since 1 kilowatt = 1000 watts, then 50 watts = $\frac{50}{1000}=0.05$ kilowatts.

Step2: Calculate the energy consumption per day

The light - bulb is used for 11 hours a day. Energy consumption $E$ (in kilowatt - hours) is given by the formula $E = P\times t$, where $P$ is power in kilowatts and $t$ is time in hours. So, $E=0.05\times11 = 0.55$ kilowatt - hours.

Step3: Calculate the daily cost

The cost per kilowatt - hour is 14 cents or $\$0.14$. The daily cost $C$ is $C = E\times0.14$. Substituting $E = 0.55$ into the formula, we get $C=0.55\times0.14=\$0.077$.

For part (b):

Step1: Convert 20 - watt LED bulb power to kilowatts

20 watts = $\frac{20}{1000}=0.02$ kilowatts.

Step2: Calculate the energy consumption of the LED bulb per day

The LED bulb is also used for 11 hours a day. So, $E_{LED}=0.02\times11 = 0.22$ kilowatt - hours.

Step3: Calculate the daily cost of the LED bulb

The daily cost of the LED bulb $C_{LED}=0.22\times0.14=\$0.0308$.

Step4: Calculate the daily savings

The daily savings $S_d$ is the difference between the daily cost of the 50 - watt bulb and the daily cost of the LED bulb. So, $S_d=0.077 - 0.0308=\$0.0462$.

Step5: Calculate the annual savings

Assuming 365 days in a year, the annual savings $S_y$ is $S_y=S_d\times365$. So, $S_y=0.0462\times365=\$16.863$.

Answer:

a. $0.077$
b. $\$16.863$