An energy-efficient lightbulb, taking in 25.0 W of power, can produce the same level of brightness as a conventional bulb operating at power 100 W. The lifetime of the energy-efficient bulb is 10,000 h and its purchase price is $17.00, whereas the conventional bulb has lifetime 750 h and costs $0.420 per bulb. Determine the total savings obtained by using one energy-efficient bulb over its lifetime as opposed to using conventional bulbs over the same time period. Assume an energy cost of $0.0870 per kilowatt-hour.
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Well, it seems like you're in quite the bright dilemma! Let me help you do the math and shed some light on this situation.
First, let's calculate the energy consumption for each bulb over its lifetime:
For the energy-efficient bulb:
Energy consumed = Power x Time
= 25.0 W x 10,000 h
= 250,000 Wh
= 250 kWh
For the conventional bulb:
Energy consumed = Power x Time
= 100 W x 750 h
= 75,000 Wh
= 75 kWh
Next, let's calculate the cost of energy consumed for both bulbs:
Cost of energy consumed = Energy consumed x Energy cost
= 250 kWh x $0.0870/kWh
= $21.75 for the energy-efficient bulb
= 75 kWh x $0.0870/kWh
= $6.52 for the conventional bulbs
Now, let's calculate the total cost for each bulb, including the initial purchase price:
Total cost for the energy-efficient bulb = Purchase price + Cost of energy consumed
= $17.00 + $21.75
= $38.75
Total cost for the conventional bulbs = (Number of conventional bulbs needed x Cost per bulb) + Cost of energy consumed
= (10,000 h / 750 h) x $0.420/bulb + $6.52
= 13.33 bulbs x $0.420/bulb + $6.52
= $5.60 + $6.52
= $12.12
Finally, we can calculate the total savings obtained by using the energy-efficient bulb:
Total savings = Total cost for conventional bulbs - Total cost for energy-efficient bulb
= $12.12 - $38.75
= -$26.63
Uh-oh! It seems like using the energy-efficient bulb actually results in a negative total savings of -$26.63. If you're looking to save some money, it might be best to stick with the conventional bulbs for now.
To determine the total savings obtained by using one energy-efficient lightbulb over its lifetime compared to using conventional lightbulbs, we need to calculate the energy consumption and cost for both types of bulbs.
For the energy-efficient lightbulb:
Power consumed = 25.0 W
Lifetime = 10,000 h
For the conventional lightbulb:
Power consumed = 100 W
Lifetime = 750 h
Step 1: Calculate the total energy consumption for both types of bulbs.
Energy consumption = Power * Lifetime
For the energy-efficient bulb:
Energy consumption = 25.0 W * 10,000 h = 250,000 Wh
For the conventional bulb:
Energy consumption = 100 W * 750 h = 75,000 Wh
Step 2: Convert the energy consumption from watt-hours (Wh) to kilowatt-hours (kWh).
Energy consumption = Energy consumption / 1000
For the energy-efficient bulb:
Energy consumption = 250,000 Wh / 1000 = 250 kWh
For the conventional bulb:
Energy consumption = 75,000 Wh / 1000 = 75 kWh
Step 3: Calculate the cost of energy consumed for both types of bulbs.
Cost = Energy consumption * Cost per kWh
For the energy-efficient bulb:
Cost = 250 kWh * $0.0870/kWh = $21.75
For the conventional bulb:
Cost = 75 kWh * $0.0870/kWh = $6.52
Step 4: Calculate the total savings by subtracting the cost of the energy-efficient bulb from the cost of using conventional bulbs.
Total savings = Cost of conventional bulbs - Cost of energy-efficient bulb
Total savings = ($6.52 + Cost of conventional bulbs) - $21.75
Now, we need to calculate the total cost of conventional bulbs. The cost of each conventional bulb is $0.420, so we divide the cost of the energy-efficient bulb by the cost per bulb and multiply it by the lifetime of the energy-efficient bulb to get the number of conventional bulbs needed.
Number of conventional bulbs = Cost of energy-efficient bulb / Cost per bulb
Number of conventional bulbs = $17.00 / $0.420 = 40.476
Since we can't use a fractional part of a bulb, we need to round up to the nearest whole number of bulbs. Therefore, we need 41 conventional bulbs.
Total cost of conventional bulbs = Number of conventional bulbs * Cost per bulb
Total cost of conventional bulbs = 41 * $0.420 = $17.22
Total savings = ($6.52 + $17.22) - $21.75
Total savings = $23.74 - $21.75 = $1.99
Therefore, the total savings obtained by using one energy-efficient lightbulb over its lifetime compared to using conventional bulbs over the same time period is $1.99.
To determine the total savings obtained by using one energy-efficient bulb over its lifetime, we need to consider the savings in energy consumption and the savings in bulb replacements.
1. Savings in energy consumption:
The energy-efficient bulb consumes 25.0 W of power, while the conventional bulb consumes 100 W. To calculate the energy savings per hour, we subtract the power consumption of the energy-efficient bulb from the conventional bulb:
Energy savings per hour = 100 W - 25.0 W = 75.0 W.
Since the energy-efficient bulb has a lifetime of 10,000 hours, the total energy savings over its lifetime can be calculated by multiplying the energy savings per hour by the lifetime:
Total energy savings = Energy savings per hour * Lifetime
Total energy savings = 75.0 W * 10,000 h
To convert the energy savings to kilowatt-hours (kWh), divide by 1,000:
Total energy savings in kWh = Total energy savings / 1,000
2. Savings in bulb replacements:
The conventional bulb has a lifetime of 750 hours, while the energy-efficient bulb has a lifetime of 10,000 hours. Therefore, the number of conventional bulbs needed over the lifetime of the energy-efficient bulb is given by:
Number of conventional bulbs = Lifetime of energy-efficient bulb / Lifetime of conventional bulb
Number of conventional bulbs = 10,000 h / 750 h
To calculate the total cost of conventional bulbs over the lifetime of the energy-efficient bulb, multiply the number of conventional bulbs by the cost per bulb:
Total cost of conventional bulbs = Number of conventional bulbs * Cost per bulb
Finally, the total savings obtained by using one energy-efficient bulb over its lifetime compared to conventional bulbs can be calculated:
Total savings = (Total energy savings in kWh * Energy cost per kWh) + Total cost of conventional bulbs - Purchase price of energy-efficient bulb
Substituting the given values:
Total savings = (Total energy savings / 1,000 kWh) * 0.0870 $/kWh + (Number of conventional bulbs * 0.420 $/bulb) - $17.00
Energy-efficient bulb:
Cost = $17.00 + $0.0870/kwh * (0.025kw * 10,000h) = $38.75.
Conventional Bulb:
# of bulbs = 10000h * (1/750)bulbs/h =
13.3333Bulbs.
Cost = 13.3333bulbs * 0.42/bulb + $0.0870/kwh * (0.10kw * 10,000h) = $92.60.
Savings = 92.60 - 38.75 = $53.85..