Hello, Mathnood768!

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.