Bryan is building his own home and is trying to determine whether he should install
a conventional heating system or a geothermal heating system in his home.
Geothermal systems, which utilize the heat of the earth to provide energy to heat the home,
costs $50 000 to install and annual operating costs would be $1200.
A conventional heating system, which utilizes electricity and natural gas to heat the home,
costs only $10 000 initially and annual operating costs would be $3600.
The operating cost of both systems increases at a rate of about 3% per year.
Simplify the equation you create as much as possible.
The resulting equation should be an exponential equation in the form:
To solve this type of equation, use the trial and error method.
Determine an equation that could be used to determine the # of years when the total cost is equivalent.
For years, the geothermal system would cost a total of:
For years, the conventional system would cost a total of:
If the total costs are equal, we have:
Take logs: .
. . . . . . . . .
The total costs are equal in about 13.7 years.