You can buy an energy-saving light bulb for $18.07, which can work for 10,000 hours. It costs you 0.8 cents to operate it for an hour. ($1=100 cents). A regular light bulb with the same intensity costs 39 cents. The light bulb can work for 1000 hours. It costs you 3.4 cents to operate it for an hour. After how many hours of operation is the energy-saving light bulb more economical?
Thank You!
Bulb A total cost (including depreciation) = 18.07 t/10,000 + 0.008 t
= 0.02607 per hour
Bulb B total cost (including depreciation) = 0.39 t/1000 + .034 t
= 0.03439 per hour
A is always less expensive, in the long run, when bulb replacement costs are included. But they probably want you to know "How soon before you save enough to pay for the energy-saving bulb?". For that answer, solve this equation:
18.07 + 0.008 t = 0.39 + .034 t
17.68 = 0.026 t
t = 680 hours, before the lamp B burns out
Nowadays, compact fluorescent energy-saving bulbs cost quite a bit less than 18.07, and the savings come much sooner.
Thank you very much! Great answer!
To determine after how many hours of operation the energy-saving light bulb becomes more economical, we need to compare the total cost of operation for both the energy-saving and regular light bulbs.
Let's start by calculating the total cost of operation for both bulbs after a certain number of hours.
For the energy-saving light bulb:
- The cost to purchase it is $18.07.
- The cost to operate it for an hour is 0.8 cents, which is equivalent to 0.008 dollars.
- It can work for 10,000 hours.
The total cost of operation for the energy-saving light bulb after 'n' hours can be calculated as:
Total Cost = Cost to Purchase + (Cost to Operate per hour x Total hours of operation)
Total Cost = $18.07 + (0.008 dollars x n)
For the regular light bulb:
- The cost to purchase it is 39 cents, which is equivalent to 0.39 dollars.
- The cost to operate it for an hour is 3.4 cents, which is equivalent to 0.034 dollars.
- It can work for 1,000 hours.
The total cost of operation for the regular light bulb after 'n' hours can be calculated as:
Total Cost = Cost to Purchase + (Cost to Operate per hour x Total hours of operation)
Total Cost = 0.39 dollars + (0.034 dollars x n)
Now, we can set up an equation and solve for 'n' to find the point at which the total cost of operation for the energy-saving light bulb becomes less than the total cost of operation for the regular light bulb.
$18.07 + (0.008 dollars x n) < 0.39 dollars + (0.034 dollars x n)
Simplifying the equation:
(0.008 dollars x n) - (0.034 dollars x n) < 0.39 dollars - $18.07
-0.026 dollars x n < -17.68 dollars
Dividing both sides by -0.026 dollars:
n > (-17.68 dollars) / (-0.026 dollars)
n > 680
Therefore, the energy-saving light bulb becomes more economical after 680 hours of operation.