A waterbed heater uses $450W$of power. It is on $25\%$of the time, off $75\%$. What is the annual cost of electricity at a billing rate of $\$0.12/kWh$?

We have given that waterbed heater uses $450W$of power. It is on $25\%$of the time, off $75\%$

We need to find that the annual cost of electricity at a billing rate.

The$1kWh$is the unit of energy, so calculating the consumed energy annually. The power is the rate where the energy is transferred. So, the energy is

$E=Pt$

The power is $P=450W=0.450KW$. So, to calculate the energy in $kWh$, we multiply the power by the time in hours. The number of hours in one year is given as

$t=(365day)\frac{24h}{1day}=8760h$

The heater is used for time $25\%$of the year, so the actual time is

$t=0.25\left(8760h\right)=2190h$

Now, putting the values for $P$and $t$into equation (1) to get the consumed energy in one year in the unit of $kWh$

$E=Pt=(0.45kW)(2190h)=985.51kWh$

The total cost will be

Annual cost = $\frac{0.12\$}{1kWh}(985.5kWh)=118.3\$$