A homeowner wants to replace their old heating system. Energy is measured in
kilowatt-hours (Wh it takes about 11,700 KWh of energy to hear the house for the winter
The current heating system uses natural gas and is coefficient which means that for
every 100 kWh of natural gasit uses it produces 60 kWh of heat. With the homeowner's
current systemIt costs $975 to beat the house. Assume that natural gas costs 50.05/kWh
and electricity costs $0.21h
The homeowner also has an air conditioner that uses 2.500 kWh of electricity per year and
produces 290 kWh of cooling for every 100 kWh it uses. They also have a water heater that
uses 4.300 kWh of electricity per year and produces 90 kWh of heat for every 100 kWh it
uses. These systems could also be replaced if there is a cheaper option, but it isn't
necessary
Here are three other types of heating systems the homeowner could replace their current
system with
A new furnace which also runs on natural gas and is more efficient. For every 100
kWh of natural gas it uses, it produces 95 kWh of heat. This system costs $5,000 to
install
. A geothermal heat pump. This system uses electricity instead of natural gas, but it
produces 4 kWh of heat for every 1 kWh of electricity it uses. It costs $14.000, but is
very low maintenance and it also replaces the air conditioner and water heater
• A-grid died solar array. This system is connected to the electrical grid so that when it
generates more energy than the house needs, the extra electricity can be sold back
to the grid. Over the whole year, the house will use as much electricity as is sold back
which means the homeowner would basically be heating and cooling the house for
free. It costs 16,000 to install

1. Which system would you recommend? Make a graph to convince the homeowner to
Switch to this system

2. How long will it take to save as much money as the new system cost?