note: please make sure to properly format your answers. all dollar figures in the answers need to include…

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places ($0.06).\na large appliance such as a water - heater is only running when it has clicked on and is actually heating water. the time your water heater is on varies according to how much you use hot water—do laundry, take showers, run the dishwasher. the national average is 3 hours per day.\na. if a water heater uses 4,200 watts, find the daily cost of running it at a cost of $0.11 per kilowatt - hour. round to the nearest ten cents.\nb. find the annual cost of running the water heater to the nearest $10.\nc. a certain energy - saving water heater sells for $1,100. it will save 36% in energy costs per year compared to the water heater from parts a and b. what will be the approximate annual cost of running this water heater? round to the nearest ten dollars.\nd. in how many years will the new water heater pay for itself?

note: please make sure to properly format your answers. all dollar figures in the answers need to include the dollar sign and any amount over 1,000 should include the comma ($2,354.67). all percentage values in the answers need to include a percentage sign (%). for all items without specific rounding instructions, round your answers to two decimal places, show both decimal places ($0.06).\na large appliance such as a water - heater is only running when it has clicked on and is actually heating water. the time your water heater is on varies according to how much you use hot water—do laundry, take showers, run the dishwasher. the national average is 3 hours per day.\na. if a water heater uses 4,200 watts, find the daily cost of running it at a cost of $0.11 per kilowatt - hour. round to the nearest ten cents.\nb. find the annual cost of running the water heater to the nearest $10.\nc. a certain energy - saving water heater sells for $1,100. it will save 36% in energy costs per year compared to the water heater from parts a and b. what will be the approximate annual cost of running this water heater? round to the nearest ten dollars.\nd. in how many years will the new water heater pay for itself?

Answer

Explanation:

Step1: Convert watts to kilowatts

Since 1 kilowatt = 1000 watts, a 4200 - watt water - heater is $\frac{4200}{1000}=4.2$ kilowatts.

Step2: Calculate daily energy consumption

The water - heater runs 3 hours per day. The energy consumption per day $E_d$ (in kilowatt - hours) is the power (in kilowatts) times the time (in hours). So $E_d = 4.2\times3=12.6$ kilowatt - hours.

Step3: Calculate daily cost

The cost per kilowatt - hour is $0.11$. The daily cost $C_d$ is the energy consumption per day times the cost per kilowatt - hour. So $C_d=12.6\times0.11 = 1.386\approx1.40$.

Step4: Calculate annual cost

There are 365 days in a year. The annual cost $C_a$ of the regular water - heater is the daily cost times 365. So $C_a = 1.40\times365 = 511\approx510$.

Step5: Calculate annual cost of energy - saving water - heater

The energy - saving water - heater saves 36% in energy costs. The cost of the energy - saving water - heater $C_{es}$ is $(1 - 0.36)\times510=0.64\times510 = 326.4\approx330$.

Step6: Calculate pay - back time

The new water - heater costs $1100$. Let the number of years be $n$. We know that the annual savings is $510 - 330=180$. We solve for $n$ in the equation $1100=180n$. So $n=\frac{1100}{180}\approx6.11\approx6$.

Answer:

a. $$1.40$ b. $$510$ c. $$330$ d. $6$