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?

Let's work through each part step by step.

### Part (a) Daily cost of keeping a 100-watt light bulb lit for 13 hours:

1. **Convert watts to kilowatts**:  
   A 100-watt bulb is $ \frac{100}{1000} = 0.1 $ kilowatts (since 1 kilowatt = 1000 watts).

2. **Calculate energy consumption in kilowatt-hours**:  
   Energy consumption $ = \text{Power (in kW)} \times \text{Time (in hours)} $.  
   For the 100-watt bulb running for 13 hours:  
   $ \text{Energy consumption} = 0.1 \, \text{kW} \times 13 \, \text{hours} = 1.3 \, \text{kWh} $.

3. **Calculate the daily cost**:  
   The cost is 13 cents per kilowatt-hour. So,  
   $ \text{Daily cost} = 1.3 \, \text{kWh} \times 0.13 \, \text{dollars/kWh} = 0.169 \, \text{dollars} $.  
   The daily cost is 16.9 cents, or $0.169 per day.

### Part (b) Savings if replaced by a 20-watt LED bulb:

1. **Energy consumption for the LED bulb**:  
   A 20-watt LED bulb is $ \frac{20}{1000} = 0.02 $ kilowatts.

2. **Energy consumed by the LED bulb in 13 hours**:  
   $ \text{Energy consumption} = 0.02 \, \text{kW} \times 13 \, \text{hours} = 0.26 \, \text{kWh} $.

3. **Daily cost with the LED bulb**:  
   $ \text{Daily cost} = 0.26 \, \text{kWh} \times 0.13 \, \text{dollars/kWh} = 0.0338 \, \text{dollars} $.  
   This is 3.38 cents, or $0.0338 per day.

4. **Daily savings**:  
   The savings per day is the difference between the costs of the two bulbs:  
   $ \text{Daily savings} = 0.169 \, \text{dollars} - 0.0338 \, \text{dollars} = 0.1352 \, \text{dollars} $ (or 13.52 cents).

5. **Annual savings**:  
   Multiply the daily savings by the number of days in a year (365 days):  
   $ \text{Annual savings} = 0.1352 \, \text{dollars/day} \times 365 \, \text{days} = 49.33 \, \text{dollars/year} $.

So, by switching to the LED bulb, you would save approximately **$49.33 per year**.

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Would you like more details on any part of this? 

Here are 5 questions to expand on this:
1. How would the calculations change if the cost per kilowatt-hour increased to 15 cents?
2. What is the total energy consumed by both bulbs in a year?
3. How much would be saved over 5 years if you switched to the LED bulb?
4. How many hours would the LED bulb need to be used to recover its cost if it costs $5?
5. What other appliances in your home could provide similar savings by switching to energy-efficient versions?

**Tip**: Switching to LED bulbs not only saves money but also reduces carbon footprint due to their energy efficiency!

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?

Learn how to calculate the daily cost of using a 100-watt light bulb for 13 hours and the potential annual savings when switching to a 20-watt LED bulb. This problem involves energy consumption, unit conversions, and cost savings, suitable for Grades 6-8.

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