National Math Trail Hydroelectric Power

1
National Math TrailHydroelectric Power

• Alexei Freire
• Carlos Filipe Gomes
• Luan Bueno
• Paulo Ramos

2
Paulo Afonso Location
3
History of Paulo Afonso City

• The region of Paulo Afonso started to be
  inhabited by Portuguese bandeirantes in the
  beginning of century XVIII. Commanded by Garcia
  Davila, they went up the river San Francisco
  and they reached lands where the city is located
  today.
• In the XIXs, Emperor D. Pedro II visited the
  waterfall of Paulo Afonso and became impressed
  with the beauty of the place. Its size commanded
  studies on the hydroelectric potential of Pablo
  Alfonso.
• Later, in 1913, Delmiro Gouveia, industrial and
  entrepreneur of the time, glimpsed the potential
  of the region, and implanted the first northeast
  hydroelectric plant called the Angiquinho Plant.
  
• The President of Brazil, Getúlio Vargas, signed a
  decree authorizing the organization of the CHESF
  - Hydroelectric Company of the San Francisco.
  CHESF became official in 1948 with the first
  general meeting of its shareholders.
• Around this time, the city of Paulo Afonso was
  born through its emancipation politics. Paulo
  Afonso is a still young city, with a great
  future. It is led by strong hands of diligent
  and glad people.

4
(No Transcript)
5
TVA Location
6
History of TVA

• President Franklin D. Roosevelt needed
  innovative solutions if the New Deal was to lift
  the U.S. out of the depths of the Great
  Depression in the 1930s. Roosevelt asked Congress
  to create a corporation clothed with the power
  of government but possessed of the flexibility
  and initiative of a private enterprise. On May
  18, 1933, Congress responded by creating the
  Tennessee Valley Authority (TVA).
• The TVA is one of Americas largest producers of
  electric power and the nations largest public
  power system. Through 158 municipal and
  cooperative power distributors, TVA serves about
  8.3 million people in a region covering Tennessee
  and parts of Kentucky, Virginia, North Carolina,
  Georgia, Alabama, and Mississippi. The TVA power
  system consists of 3 nuclear generating plants,
  11 coal-fired plants, 29 hydroelectric dams, 5
  combustion-turbine plants, a pumped-storage
  plant, and about 27,000 kilometers of
  transmission lines.
• TVA continues to strengthen its position as an
  energy leader in price, reliability, efficiency,
  and environmental stewardship as it helps lead
  the utility industry into the 21st century.

7
(No Transcript)
8
The Problem

• The Paulo Afonso facilities produced
  3,900,000kw of energy in the year 2002 and has
  increased at a rate of 250,000kw per year. TVA
  produced 390,000,000kw in the year 2002 and has
  increased at a rate of 50,000kw per year. How
  long will it take Paulo Afonso to produce the
  same amount of energy that TVA produces? What
  would be the amount of energy they would be
  producing in that year?  

9
(No Transcript)
10
The Solution
Paulo Afonso Production
TVA Production
P250,000Y2390,000,000
P1250,000Y1 3,900,000
11
P1250,000Y1 3,900,000
P250,000Y2390,000,000
To find in how many years the production of
energy will be equal we solve the system
P1P2
250Y3900 50Y390000 200Y 386100 Y 1930.5
years
12
To find how much they will produce in that year
we substitute the value of the year in the
equation
P1250,000Y1 3,900,000 P250,000
(1930.5)3,900,000 P 783,525,0003,900,000 P
783,915,000kw
13
So they will produce the same amount of energy
783,915,000kw
In
1930.5 years