energy mathematics compounding and exponential growth rate

Energy Mathematics

Compounding and Exponential Growth

Rate

Change in Price 4.12 – 2.80 Original Price 2.80

47 % Increase

== .47

Change in Price 1.61 - 4.12 Original Price 4.12

61% Decrease

= =-.61

Gasoline Prices --- August 2007 to July 2008

Gasoline Prices --- July 2008 to December 2008

20 Folds -- 100 meters

30 Folds – 107 km or 65 miles

37 Folds -- Diameter of the Earth

2n

28

2 - 1

nTotal Number of Coins =

2 - 1

7

2 - 114

Pennies = $

Pennies = $

2 - 17

2 - 114

Pennies = $ 1.27

Pennies = $ 163.83

2 - 1

21

2 - 130

Pennies = $

Pennies = $

2 - 1

21

2 - 130

=

$20,971.51

=

$10,737,418.23

I = PrtI = InterestP= Principle or original investmentr = rate of interestt = time

I = PrtI = ($100)(0.05)(1) = $105.00

I = ($100)(0.05)(2) = $110.00

CompoundiCompoundingng Growth on Growth

$ 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

Money in Account = (P)(1+r)n

P= Principle or original investmentr = rate of interest n = number of years

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

Savings accounts: 2-3%

Car Loans: 5-15%

Credit Card Interest: 8-22%

World Population growth = 1.2%

Reasons for Energy Growth

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

.

A gallon of gasoline is about

125,000 Btu

.

One quad is 1015 Btu 1,000,000,000,000,000 Btu

4 days of U.S. Energy Use

1950 – 34.6 quads

1970 – 67.8 quads

20 Years33.2 quads

Increase

End Energy Consumption =

(Beginning Consumption)(1+growth rate)n

Energy Growth Rate =

End ConsumptionBeginning Consumption

1 n

( ) - 1

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

Energy Growth Rate =

End ConsumptionBeginning Consumption

1 n

( ) - 1

Energy Growth Rate = 1950 - 197067.

834.6

1 . 20

( - 1 =

)

Annual Energy Growth Rate

1950-1970 = 3.4%

Energy Growth Rate = 1973 - 198373.

075.7

1 . 10

( - 1 =)

Annual Energy Negative Growth Rate

1973-1983 = - 0.36%

Energy Growth Rate = 1988 - 200899.

382.8

1 . 20

( - 1 =)

Annual Energy Growth Rate

1988-2008 = 0.9%

Why did United States Energy Demand Drop?

Per Capita Energy Growth Rate 1981 – 332 MBTU 2011 – 312 MBTU

312 MBTU

332 MBTU

1 . 30

( - 1 =)

Per Capita Energy Growth Rate = 1981 - 2009

312332

1 . 30( - 1 =)

Per Capita Energy Growth Rate = 1981 - 2011

0.94

1 . 30( -1 = (0.997 – 1)= - .003 - 0.3% growth rate

)

United States Energy Demand

2035?

U.S. Energy Information Administration

Predicts Annual Energy Growth of

0.5% till 2035

Calculate U.S. Energy Demand by the year 2035

End Energy Consumption =

(Beginning Consumption)(1+growth rate)

Energy Consumption 2035 =

(97.5) (1 + [0.005])22 =

(97.5) (1.005)22 = (97.5) (1.12) = 109.2 quads