Question

An energy-efficient lightbulb, taking in 27.0 W of power, can produce the same level of brightness as a conventional lightbulb operating at power 100 W. The lifetime of the energy-efficient bulb is 10 000 h and its purchase price is $4.60, whereas the conventional bulb has lifetime 750 h and costs $0.50 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 $0.20 per kilowatt-hour.

Answer 1

Answer:

$148.4

Step-by-step explanation:

Given:

Power consumed by the energy-efficient lightbulb = 27.0 W = 27.0 × 10⁻³ kW

Power consumed by the conventional lightbulb = 100 W = 100 × 10⁻³ kW

Lifetime of the energy-efficient lightbulb = 10,000 h

Lifetime of the conventional lightbulb = 750 h

Cost of the energy-efficient lightbulb = $4.60 per bulb

Cost of the conventional lightbulb = $0.50 per bulb

Energy cost = $0.20 per kilowatt-hour

Now,

The total cost of  energy-efficient lightbulb for 10,000 hours

= cost of bulb + energy cost

= $4.60 + ( 27.0 × 10⁻³ kW × $0.20 kW/h × 10,000 h)

= $4.60 + $54

= $58.60

Now,

For the life of 10,000 hours number of conventional bulbs required

= $\frac{\textup{Total lifetime required}}{\textup{Lifetime per bulb}}$

= $\frac{\textup{10,000}}{\textup{750}}$

= 13.33 ≈ 14 bulbs

Thus,

The total cost of  conventional bulb for 10,000 hours

= cost of bulb + energy cost

= ( $0.50 × 14 ) + ( 100 × 10⁻³ kW × $0.20 kW/h × 10,000 h)

= $7 + $200

= $207

Therefore,

The total savings = $207 - $58.60 = $148.4