Absolutely, let's walk through the calculation step-by-step:
### Step 1: Determine the Total Hours in a Month
First, we need to calculate the total number of hours the bulb is left on within a month (considering 30 days):
[tex]\[
\text{Total hours} = 30 \, \text{days} \times 24 \, \text{hours/day} = 720 \, \text{hours}
\][/tex]
So, the bulb is on for 720 hours in a month.
### Step 2: Convert the Power from Watts to Kilowatts
Next, we need to convert the power rating of the bulb from watts to kilowatts, since electricity costs are given per kilowatt-hour (kWh):
[tex]\[
\text{Power in kilowatts (kW)} = \frac{25 \, \text{watts}}{1000} = 0.025 \, \text{kW}
\][/tex]
### Step 3: Calculate Total Energy Consumption
Now, calculate the total energy consumed by the bulb over the month in kilowatt-hours (kWh):
[tex]\[
\text{Total energy consumption (kWh)} = \text{Power (kW)} \times \text{Total hours} = 0.025 \, \text{kW} \times 720 \, \text{hours} = 18.0 \, \text{kWh}
\][/tex]
So, the bulb consumes 18.0 kWh in a month.
### Step 4: Calculate the Total Cost
Then, we calculate the total cost of the electricity used. Given the cost of electricity is 20 cents per kWh, we convert this to dollars (since 20 cents is \[tex]$0.20):
\[
\text{Total cost} = \text{Total energy consumption (kWh)} \times \text{Cost per kWh} = 18.0 \, \text{kWh} \times 0.20 \, \text{dollars/kWh} = 3.6 \, \text{dollars}
\]
### Step 5: Round the Total Cost
Finally, we round the total cost to the nearest cent. In this case, the cost is already given to be exactly \$[/tex]3.6, so no further rounding is needed.
### Conclusion
The monthly energy cost of leaving a 25-Watt bulb on continuously, if electricity costs 20 cents per kWh, is \$3.60.
