To solve this, we need to calculate the energy consumption and cost for both the 100-watt incandescent bulb and the 25-watt LED bulb.

Step 1: Calculate energy consumption for the 100-watt bulb

• Power of the bulb = 100 watts = 0.1 kilowatts (since 1 kilowatt = 1000 watts)
• Time in a week = 7 days × 24 hours/day = 168 hours

Energy consumed in a week (in kilowatt-hours) = Power (in kW) × Time (in hours) $E_{\text{incandescent}} = 0.1 \, \text{kW} \times 168 \, \text{hours} = 16.8 \, \text{kWh}$

Step 2: Calculate the cost for the 100-watt bulb

The cost is calculated by multiplying the energy consumed by the rate charged by the utility company.

Cost = Energy consumed × Rate $\text{Cost}_{\text{incandescent}} = 16.8 \, \text{kWh} \times 0.15 \, \text{USD/kWh} = 2.52 \, \text{USD}$

So, it costs $2.52 to keep the 100-watt bulb on for a week.

Step 3: Calculate energy consumption for the 25-watt LED bulb

• Power of the LED bulb = 25 watts = 0.025 kilowatts
• Time in a week = 168 hours

Energy consumed in a week (in kilowatt-hours) = Power (in kW) × Time (in hours) $E_{\text{LED}} = 0.025 \, \text{kW} \times 168 \, \text{hours} = 4.2 \, \text{kWh}$

Step 4: Calculate the cost for the 25-watt LED bulb

Cost = Energy consumed × Rate $\text{Cost}_{\text{LED}} = 4.2 \, \text{kWh} \times 0.15 \, \text{USD/kWh} = 0.63 \, \text{USD}$

So, it costs $0.63 to keep the 25-watt LED bulb on for a week.

Step 5: Calculate yearly savings

To find how much you save in a year by switching to the LED bulb:

• Cost difference per week = $2.52 \, \text{USD} - 0.63 \, \text{USD} = 1.89 \, \text{USD}$
• Savings per year = Cost difference per week × 52 weeks $\text{Savings}_{\text{yearly}} = 1.89 \, \text{USD/week} \times 52 \, \text{weeks} = 98.28 \, \text{USD/year}$

Thus, you will save $98.28 per year by switching to the LED bulb.

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Would you like more details or have any questions? Here are some related questions:

1. How do energy efficiency ratings compare for different types of light bulbs?
2. What is the environmental impact of using energy-efficient bulbs like LEDs?
3. How long do LED bulbs typically last compared to incandescent bulbs?
4. What other household appliances use significant energy and how can they be made more efficient?
5. How can you calculate the cost savings for switching multiple light bulbs in your home?

Tip: Energy-efficient LED bulbs last much longer and use significantly less electricity, making them a smart investment despite the higher upfront cost.