Your utility company charges 11 cents per​ kilowatt-hour of electricity.
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 15 watts of​ power?


To solve these problems, we'll first calculate the daily cost of using a 100-watt light bulb for 13 hours each day. Then, we'll find the annual savings when replacing it with an LED bulb that uses 15 watts.

### a. Daily Cost of a 100-Watt Light Bulb

1. **Convert watts to kilowatts**:
   \[
   \text{Power in kilowatts} = \frac{100 \, \text{watts}}{1000} = 0.1 \, \text{kW}
   \]

2. **Calculate the daily energy consumption**:
   \[
   \text{Energy consumption (kWh)} = \text{Power (kW)} \times \text{Time (hours)}
   \]
   \[
   \text{Energy consumption} = 0.1 \, \text{kW} \times 13 \, \text{hours} = 1.3 \, \text{kWh}
   \]

3. **Calculate the daily cost**:
   \[
   \text{Daily cost} = \text{Energy consumption (kWh)} \times \text{Cost per kWh}
   \]
   \[
   \text{Daily cost} = 1.3 \, \text{kWh} \times 0.11 \, \text{USD/kWh} = 0.143 \, \text{USD} \, (\text{or 14.3 cents})
   \]

### b. Annual Savings with an LED Bulb

1. **Calculate the power consumption of the LED bulb**:
   \[
   \text{Power in kilowatts for LED} = \frac{15 \, \text{watts}}{1000} = 0.015 \, \text{kW}
   \]

2. **Calculate the daily energy consumption for the LED bulb**:
   \[
   \text{Energy consumption (kWh)} = 0.015 \, \text{kW} \times 13 \, \text{hours} = 0.195 \, \text{kWh}
   \]

3. **Calculate the daily cost for the LED bulb**:
   \[
   \text{Daily cost for LED} = 0.195 \, \text{kWh} \times 0.11 \, \text{USD/kWh} = 0.02145 \, \text{USD} \, (\text{or 2.145 cents})
   \]

4. **Calculate the annual cost for both bulbs**:
   \[
   \text{Annual cost for 100-watt bulb} = 0.143 \, \text{USD/day} \times 365 \, \text{days} = 52.195 \, \text{USD}
   \]
   \[
   \text{Annual cost for LED bulb} = 0.02145 \, \text{USD/day} \times 365 \, \text{days} = 7.82925 \, \text{USD}
   \]

5. **Calculate the annual savings**:
   \[
   \text{Annual savings} = 52.195 \, \text{USD} - 7.82925 \, \text{USD} = 44.36575 \, \text{USD}
   \]

### Final Answers:
- **a.** The daily cost of keeping a 100-watt light bulb lit for 13 hours is **14.3 cents (0.143 USD)**.
- **b.** The annual savings if replaced with a 15-watt LED bulb is **44.37 USD**.

Would you like more details or have any other questions?

### Related Questions to Expand Your Understanding:
1. What would the savings be if the electricity cost was different, say 15 cents per kilowatt-hour?
2. How much would it cost to run multiple 100-watt bulbs for different durations, such as 5 hours or 20 hours daily?
3. How does the lifespan of a standard bulb compare to an LED bulb, and how does that impact cost over time?
4. If you used a dimmer switch to reduce the wattage of a 100-watt bulb, how would that affect daily costs?
5. What are some other ways to reduce electricity costs besides switching to LED bulbs?

**Tip:** Switching to energy-efficient appliances and bulbs can significantly reduce your electricity bill over time!

Learn how to calculate the daily cost of using a 100-watt light bulb for 13 hours and the annual savings when replacing it with a 15-watt LED bulb. Includes detailed step-by-step calculations for electricity consumption and cost. Suitable for high school students studying energy efficiency and cost calculations.

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