Algebra Lab

Coal Mining and Electricity

This is a study of electricity generated by the Four Corners Power Plant and some of the cities it services.

Nahat’á (planning) Mathematical Topics Learn or review mathematical concepts and skills needed to study electricity supply and demand.  See the menu at the left. Information Population The Four-Corners Power Plant helps provide, among others, these major cities with electricity: Phoenix; Tucson; Albuquerque; El Paso; and Los Angeles.  The Table below provides populations (in thousands) of these cities in the indicated years.   1970 1980 1990 Phoenix 584 790 983 Tucson 263 331 405 Albuquerque 245 332 385 El Paso 322 425 515 Los Angeles 2812 2969 3485 Units 1 watt is a unit of electrical energy 1 kilowatt = 103 watts. 1 kilowatt-hour (kwh) is a measure of the amount of electrical power, it is the amount generated at a rate of 1 kilowatt for one hour.  For example, if electricity is being produced at the rate of 5 kilowatts, then in one hour, 5 kilowatt-hours of electricity will be generated Coal and Electricity Usage On the average, a person in the United States uses electricity at the approximate rate of .381 kilowatt. The Four-Corners Power Plant produces electricity by burning coal from the Navajo mine. The coal from the Navajo mine produces approximately 1.4 kwh of electricity for each pound of coal burned.  The maximum production rate for the Four-Corners Power Plant at any time is 2040 x103 kilowatts.

Iiná (living) Apply mathematical knowledge and applets to analyze electricity supply and demand.  Questions 1.  Make points from each data set in the table, one for each city.  The first coordinate will be the year, denoted by t, with t = 0 in the year 2000.  The second coordinate will be city population, denoted by the first letter of the city. 2.  Using regression fit each data set with the type of equation specified below.  Graph each of the equations on separate screens. A)  Phoenix, linear B)  Tucson, linear C)  Albuquerque, linear D)  El Paso, linear E)  Los Angeles, exponential 3.  Combine the five pieces to obtain a new equation that gives the total population of the cities.        4.   Estimate the current total combined population of all the cities. 5.  If all electricity were produced from coal, how much coal would it take to supply one person with electricity for one year? 6.  What is the maximum number of people that could be supplied electricity from the Plant at any given time? 7.  Could the Power Plant provide enough electricity for all five cities now?