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 utilize the heat of the earth to provide energy to heat the home. The geothermal system costs $50 000 to install but annual operating costs would be $1200.

A conventional heating system, which utilizes electricity and natural gas to produce heat for the home, costs only $10 000 initially but annual operational costs would be $3600.

The operational 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 formm=^{x}n. 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:

I'm really bad at math and I'm not even sure where to start...

I figured out this though:

Sn = 1200 (0.03^n - 1) / 0.03 - 1

Formula for the sum of the annual operating costs fornyears for a geothermal system.

Sn = 3600 (0.03^n - 1) / 0.03 - 1

Formula for the sum of the annual operating costs fornyears for a conventional system.

Any help would be appreciated!