Anaerobic Digestion of Manure to Yield Methane

Anaerobic methane digesters has been used for years to reduce energy costs on farms in Europe and North America. The digesters operate by using anaerobic bacteria to break down animal waste. During the process, which typically uses a tank heated to about 100℉ (38℃) to speed the reactions, raw manure is broken down and methane is produced. The methane can then be used to generate electricity or produce heat.

For a dairy farm in with cows, the cost of installing a digester is approximately $. Assume that the farm uses kWh of electricity each year at a cost of $ per kWh. The waste from a single cow can produce 3.0 kWh of electricity each day. Assume that the cost of electricity remains constant and the farmer uses all of the manure from the cows in an anaerobic digester to produce electricity on the farm.

Calculate the number of kWh of electricity that can be produced in one year on the farm in

The amount of money the farmer in can save in one year, NOT counting the installation cost of the digester. (You may round your answer to the nearest $1,000 on the APES exam, but the program does not round here.)

The amount of time, in years, that it will take to recover the cost of installing an anaerobic digester on the farm in . You may round your answer to the nearest whole number.

Calculate the minimum number of cows the farm in would need to produce 800,000 kWh of electricity per year. You may round your answer to the nearest whole number.