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A particular electric utility charges customers different rates depending on their daily rate of energy consumption: $0.05/kWh up to 20 kWh, and $0.10/kWh for all energy usage above 20 kWh in any 24-hour period. (a) Calculate how many 100 W light bulbs can be run continuously for less than $10 per week. (b) Calculate the daily energy cost if 2000 kW of power is used continuously.

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Answer:

(a) the number of 100W light bulbs is 11

(b) the daily cost of 2000 kW is $4,800

Step-by-step explanation:

charge of energy consumption up to 20 kWh = $0.05/kWh

charge of energy consumption above 20 kWh = $0.10/kWh

(a) number of 100 W light bulbs that can be run continuously for less than $10 per week

Total energy consumed by 100 W in 1 week = (0.1 kW) x (7 x 24 h)

                                                                          = 16.8 kWh

Charge associated with this consumption = $0.05/kWh

let the number of 100 W light bulbs = n

[tex]n(\frac{\$ 0.05}{kWh} \times 16.8 kWh) = \$10\\\\n(0.84) = 10\\\\n = \frac{10}{0.84} \\\\n = 11.9[/tex]

Since 0.9 is not a whole number, the number of 100 W light bulbs is 11.

(b) if 2000 kW is used continuously

total energy consumption = 2000 kW x 24 h = 48,000 kWh

The daily cost is calculated as;

[tex]= \frac{\$0.10 }{kWh} \ \times \ 48,000 kWh\\\\= \$ 4,800[/tex]

Cetacea

A particular electric utility charges customers different rates depending on their daily rate of energy consumption :

(a) the number of 100W light bulbs is 11

(b) the daily cost of 2000 kW is $4,800

"Energy Consumption"

Given :

Charge of energy consumption up to 20 kWh = $0.05/kWh

Charge of energy consumption above 20 kWh = $0.10/kWh(

Part a)

Number of 100 W light bulbs that can be run continuously for less than $10 per week

  • Total energy consumed by 100 W in 1 week = (0.1 kW) x (7 x 24 h)
  • Total energy consumed by 100 W in 1 week = 16.8 kWh

Charge associated with this consumption = $0.05/kWh

Let the number of 100 W light bulbs = n[tex]n\left(\frac{\$0.05}{kWh}\cdot16.8kWh\right)=\$10\\n\left(0.84\right)=10\\n=\frac{10}{0.84}\\n=11.9[/tex]

Since 0.9 is not a whole number.

Thus, the number of 100 W light bulbs is 11.

Part b)

2000 kW is used continuously

Total energy consumption = 2000 kW x 24 h

Total energy consumption  = 48,000 kWh

The daily cost is calculated by:

[tex]\frac{\$0.10}{kWh}\cdot48000\ kWh

Daily cost=\$4800[/tex]

Learn more "Energy Consumption":

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