Energy Mathematics Compounding and Exponential Growth Rate

1. Energy Mathematics Compounding and Exponential Growth Rate

3. Gasoline Prices --- August 2007 to July 2008 Change in Price 4.12 – 2.80 Original Price 2.80 47 % Increase = = .47 Gasoline Prices --- July 2008 to December 2008 Change in Price 1.61 - 4.12 Original Price 4.12 61% Decrease = -.61 =

4. 20 Folds -- 100 meters 30 Folds – 107 km or 65 miles 37 Folds -- Diameter of the Earth

5. n 2 8 2

6. Total Number of Coins = n 2 - 1

7. 7 2 - 1 Pennies = $ 14 2 - 1 Pennies = $

8. 7 2 - 1 Pennies = $ 1.27 14 2 - 1 Pennies = $ 163.83

9. 21 2 - 1 Pennies = $ 30 2 - 1 Pennies = $

10. 21 2 - 1 = $20,971.51 30 2 - 1 = $10,737,418.23

11. I = Prt I = Interest P= Principle or original investment r = rate of interest t = time

12. I = Prt I = ($100)(0.05)(1) = $105.00 I = ($100)(0.05)(2) = $110.00

13. Compounding Growth on Growth

14. $ 100.00 @ 5% -- $5.00 First Year $105.00 $ 105.00 @ 5% -- $5.25 Second Year $110.25 $ 110.25 @ 5% -- $5.51 Third Year $115.76 $ 200 in 14.4 years

15. Money in Account = (P)(1+r)n P= Principle or original investment r = rate of interest n = number of years

16. Money in Account = (P)(1+r)n Money = (100) (1+ 0.05)3 Money = (100) (1.05)3 Money = (100) (1.1576) Money = $115.76

17. Savings accounts: 2-3% Car Loans: 5-15% Credit Card Interest: 8-22% World Population growth = 1.2%

18. Reasons for Energy Growth

19. Btu is the amount of heat liberated from a wooden kitchen match.

20. . A gallon of gasoline is about 125,000 Btu

21. . One quad is 1015 Btu 1,000,000,000,000,000 Btu 4 days of U.S. Energy Use

22. 1950 – 34.6 quads 1970 – 67.8 quads

23. 20 Years 33.2 quads Increase

24. End Energy Consumption = (Beginning Consumption)(1+growth rate) n

25. Energy Growth Rate = 1 n ) ( End Consumption Beginning Consumption - 1

26. Year Energy Consumption 1950 34.6 quads 1970 67.8 quads 1973 75.7 quads 1983 73.0 quads 1988 82.8 quads 2008 99.3 quads 2030 ??? quads

27. Energy Growth Rate = 1 n ) ( End Consumption Beginning Consumption - 1

28. Energy Growth Rate = 1950 - 1970 1 . 20 ( ) 67.8 34.6 - 1 =

29. Annual Energy Growth Rate 1950-1970 = 3.4%

30. Energy Growth Rate = 1973 - 1983 1 . 10 ( ) 73.0 75.7 - 1 =

31. Annual Energy Negative Growth Rate 1973-1983 = - 0.36%

32. Energy Growth Rate = 1988 - 2008 1 . 20 ( ) 99.3 82.8 - 1 =

33. Annual Energy Growth Rate 1988-2008 = 0.9%

34. Why did United States Energy Demand Drop?

35. Per Capita Energy Growth Rate 1981 – 332 MBTU 2011 – 312 MBTU 1 . 30 ) ( 312 MBTU 332 MBTU - 1 =

36. Per Capita Energy Growth Rate = 1981 - 2009 1 . 30 ( ) 312 332 - 1 =

37. Per Capita Energy Growth Rate = 1981 - 2011 1 . 30 ( ) 0.94 • 1 = (0.997 – 1)= - .003 • - 0.3% growth rate

38. United States Energy Demand 2035?

39. U.S. Energy Information Administration Predicts Annual Energy Growth of 0.5% till 2035 Calculate U.S. Energy Demand by the year 2035

40. End Energy Consumption = (Beginning Consumption)(1+growth rate)

41. Energy Consumption 2035 = (97.5) (1 + [0.005])22 = (97.5) (1.005)22 = (97.5) (1.12) = 109.2 quads