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Issues 7 10 12 Math Solutions - .u.u—.4 Issue 7 OIL AND...

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Unformatted text preview: _...... .u.u—..4-. Issue 7 OIL AND NATURAL GAS Question 7-1: According to the Department of Labor, the Consumer Price Index is a measure of the representative cost of a “basket” of goods and services. It stood at 127.4 in 1990, and had reached __201 by mid-2006.3 Therefore, by what percent had the CPI increased over that sixteen--year interval? (201-127.4)1127.4 = 0.578 = 57.8 “A: Question 7—2: To determine the 2006 price that would be equivalent to a 1990 price of $60 per barrel, multiply the 1990 minimum price by l + the percentage you just calculated. What would be the 2006 price needed to “guarantee” 6'700 million barrels of ultimately recoverable oil? _,_,____, 601 l.578==$94. s ___*__m___ _ ____ - Question 7-4: What is today’s wofld price for oil? Check the web, a daily newspaper, or business network. Question 7-5: In what year, starting from 2005, would the world run out of oil in this scenario? 1190 billion barrelsBl— billion barrels per year = 38.4 years 2005 + 38.4 = The year 2043 Question 7—6: What was the percentage increase of oil consumption from 1986 to 2006‘? (86 - 61.8}!613 = 0.392 = 39.2% Question 7—7: What was the average annual growth rate in oil consumption for the 20-year period from 1986 to 2006'? (The most accurate way to calculate the average rate of increase is to use the fonnula r = (1ft)1n(NfNo). r = (in) ln(N!No} = {1!20)in[(86 x 10‘);(61.s x 10%] = 0.016 = 1.6%: Qer yea: Question 7—8: What is the doubling time for the increase you just calculated? _ 70l1-6 = 43.8 years Question 7-9: How many millions of barrels of oil a day will the world be consuming when it is double the 2006 level? Over 1'70 million barrels a da - In discussion this answer, it could be useful to talk about accuracy and precision. Question 7-10: To estimate the total amount of oil that was consumed-owe]: a given period, first convert the beginning and ending rates of consumption (say, 80 million barrels a day) to barrels per year. Then add the beginning and ending consumption rates together and divide by 2. Finally, multiply this number by the number of years. How much oil will have been consumed during that period you determined for Question 9‘? , The period is about 44 ears- The world was consuming 85 mbfd in gang and would be consuming 1'70 mbd in 44 ears: The average rate of consumption would be zssrz or about 125 mbd. Multiply this bx 365, ignoring leap years, to get average annual consumption. Total consumed over that interval would be 2,055 billion barrels. How does this compare to total oil reserves atthe end of 2004 (ii-om p. 30)? Discuss- Question 7-11: roven reserves in 2004'. The discussion should be It is nearly twice as much as the total interesting. , Question 7-13: The mean estimate by the U.S. Geological Survey of recoverable oil in the Arctic National Wildlife Refuge (ANWR) is about 10.3 billion barrels without regard to price- Based on the mid-2006 U.S. annual consumption rate of about 7.7 billion barrels of oil per year, how many months would these new fields last? It would be a 1 113 zear supply, or 16 months, assuming ANWR had to supply all the U.S. demand. n Question 7—17: Baseo un I. dun: 1‘3, inc statement above, and assuming no increase in uelnand, how many years‘ worth of natural gas does the world have left? Proven reserves from Table 7-3 were 6,040 TCF. Consumption was 92 TCFlyear. Division yields about 66 years- Question 7-18: How many years’ supply does the U.S. have left, based on reserves from Table 7—3. The U.S- uses about 22 TCFItear, and had proven reserves of 189 TCF- Division yields an 8.6 year supply, assuming no new discoveries or developments- Question 7-19: Global gas consumption is projected by EIA to grow at 2.3%!year. Use the doubling time formula to project how long at this rate it will take for consumption of natural gas to double from 2002’s 92 TCF/year- T = 703.3 = 30.4 years. Issue 10 SUSTAINABLE ENERGY: IS THE ANSWER BLOWING IN THE WIND? Question 10—1: What was the percentage increase in energy consumption from 197071988? 1 9887 2004? Is the rate of increase of U-S- energyr consumption rising or falling? 1970—1988: (80.2 — 66.4) f 66.4 = -297, or 20.7% increase- 1988—2004: ( 100-2 -80-2)i80.2 = .299 or i§.9% increase- Question ] 0—2: What was the average yearly increase in energy consumption over the period 1 970—2004? (Use the forn'iula r : (1ft)ln(Nz'Nn); see Using Mala in Environmental Issues, pages 6—8)- 1- = (l!t)]n(NfNo) r = 184 In (100-2f66.4) = 12'34 (0.41)- i 0-012 = 1-2“.4- '— Question 10—3: What is the doubling time ofenergy consumption, based on your answer to Question 1 0—2? (Use the formula T = 702%). T= TOIr = 70f1.2 = 58 years- .— Question 18—4: Based on the 1970—2004 rate of increase, estimate U-S- energy use in 2010, 2020- and 2030- Use the compound interest forn'lula: future value = present value x (e)n- N (2310) = NO X (3)1,l N = 100-2 3: e “”2 “’ = 107,68 Quads _ Nana; = 100.2 x em” " “' = 1 18.53 Quads N{2030) = 100.2 x emu!“ = 133-6 Quads Question 10—5: Total electric power generation from solar and wind sources from 2000—2004 are given in Table 1 0—1 . What was the annual rate of increase in electric power generated from solar and wind systems from 2000—20-04? Use 1' Z (l!t)ln(NfNo) Fgr wind: r = 1,6. In (-143i-057) = 1/. In (2.51) = M. (-92) = 0-23 = 230/“ From solar r 2 1/5; In (0-063!0.066) = —0.012, or a drop of1.2"/B \ Question 1 0—6: What is the doubling tiine of electricity production from—3 wind systems, based on the data for 2000—2004? T = 70123 2 3 xears “fl Question 10-7: Assume this rate of increase were to extend to 2020. Project the amount of electricity, in quad BTU that would be produced from wind in 2020. Use future value : present value x (e) . I‘J=l"~loxel't = 0.143 x e (‘23 " '6’ = 5.7 Quads produced in 2020 Question 10-8: How does the production figure you got in your answer to Question 10-7 compare With the energy use for 2020 you calculated in Queshm l0-4? 1 18.5 Quads projected “m 5.7 Quads from wind in 2020. Question 10—12: What wallhe average cost to install one kilowatt of wind energy in 2004‘? Divide the total investment, in dollars, by the new installed capacity. Express your answer in dollars per kilowatt. Div'de Industry instalied 2,400 MW in 2005, e ual to 2400000 kW- Cost was $3 billion. 3, 0, , , 0 : approx. $12501kw. Question 10-14: Based on information in the paragraph above, what is the annual electricity consumption of an “average” house in the 11.3.? 4 million kWh/y divided by 400 III-es = about 10,000 kWh/y “average” electricity consumption. Question 10—15: Based on thepm'agmph above 10-14, and the total US. electricity consumption in kWh, how many 1.5 MW wind turbines would be required to satisfy this demand? Electricity demand is about 4 trillion kay. Each turbine can produce 4 million kWh/y. 4,000,000,000,000/4,000,000 = 1 million 1-5 kW wing turbines. Question 10-16: Taking the average annual household electricity consumption at 10,000 kWh, how many homes could theoretically be provided electricity through wind power development in the top 5 states alone? Potential is 5 400 billion kWh / 10 000 kWh or he == 540 x 10"3 homes. Question 10-17: According to the US. Energy Information Administration”, the U.S. consumed 3,953,000,000,000 kWh ofelectricity in 2004. How does this compare to the wind energy potential of the top five states in Table 10-3? To five states 5520 x 109 ' ' " entire US. electrici demand (3,953 x 10 kWh/y). Issue 12 MOTOR VEHICLES AND THE ENVIRONMENT I Question 12-1: By what percent did hybrid sales increase between 2000 and 2006? (252,636 — 9,350) 9,350 = 26.02 '1’. Sales between 2000 and 2006 increased by a factor of 26. That could also be expressed as 2600%. Question 12-2: What is the doubling time for hybrid sales, based on the increase fi'om 2000 to 2005‘? To answer this question, you must first calculate r. Use: 1' = (lit)1n(N/'No) = 1f5 1n (205,749f9350) = 0.618 2 6] .8'3/6 per year T270lr= 70K61.8 : 1.13 years __/ The students may point out that it is obviously impossible to sustain such a growth rate! This question shows clear-1y, we hope, the limitations of mathematics and forecasting- Question 12—3: Based on question 12—2, forecast hybrid sales in 2015. This can be done two ways. If we round the doubling time to 1 year, then in “i 0 years the sales will double 10 times, which is 2.10 'x 108 hybrids. A more accurate way involves using: N = No x err = 205,749 x e‘O-é'gx '03 = 9.94 X107 Question 12—6: Calculate the percentage of light trucks and SUVs out ofrtotal vehicle sales and fill in the table below. To answer this question, students should assume SUVs are a kind of light truck and so they should not add SIJ'Vs to light trucks to get total annual sales- Thus, for 1975, total sales would be 090 m’llion obtained addin car sales to l' ht truck sales only. {2/0 SUVS 1 % Li _ht Trucks 20-9 _- _- m - - . . _ht—I H404 LAJXWNN NOON-Nook- mqwmmk llm MOON \ON-h i ...
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