energy mathematics compounding and exponential growth rate
DESCRIPTION
Energy Mathematics Compounding and Exponential Growth Rate. 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 - PowerPoint PPT PresentationTRANSCRIPT
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