7.2.2: The Power of Nature Over the past ten years the use of renewable sources of energy has become more popular. Both solar and wind energy are becoming more globally accepted as new sources of energy Below is data on annual world wind energy production and world photovoltaic production (solar energy) from 1997 and data on atmospheric Co. emissions from 1997 Wind Power Global Wind Power Production 100 Year Production (MW) 1997 7.475 80 1998 9.663 70 1999 13.696 2000 18.039 2001 24.32 2002 31.164 2003 39.29 2004 47.693 2005 59.033 2006 74.153 1990 2006 2007 93.849 Year http://www.wwindea.org home/index.php W()= 0.0612361 - 367.0021 +733178.31 - 488238151 60 Production (MW) 50 40 30 20 10 2000 2004 Global Solar Power Production 1800 1600 1400 1200 Solar Power Year Production (MW) 1997 126 1998 153 1999 201 2000 288 2001 391 2002 560 2003 742 2004 961 2005 1211 2006 1504 2007 1818 Production (MW) 1000 800 600 400 200 1998 2000 2004 2008 2002 Year http://www.carth-policy.org/Indicators/2004/indicator12_data.htm $(1) - 16.7821 -67026.31 +66924727 TIPS4RM: MHF4U - Performance Task 2008 7.2.2: The Power of Nature (continued) CO, Emissions over Time COEmissions Mean CO2 Year Emissions (ppm) 1997 363.35 1998 366.29 1999 368.24 2000 369.34 2001 370.92 2002 372.91 2003 375.61 2004 379.88 2005 379.51 2006 382.21 2007 383.84 375 - Mean CO, Emissions (ppm) 370- 365 380 355- 1998 2000 2004 2006 2002 Year CO, (1) = 0.0091465r? 34.57077 +32923 TIPSARM: MHF4U -Performance Task 2008 31 7.2.2: The Power of Nature (continued) 1. You determined the date 2030 is when the concentration of carbon dioxide will reach 450 ppm. How much total energy from renewable resources (solar and wind energy) will be produced at that time? 2. Using the three given functions for Wind Power, Solar Power and CO, Emissions, determine a combination of those functions that will model the rate at which CO2 emissions are changing with respect to total energy produced from wind and solar power. (Do not simplify the expression.) 3. Use graphing technology to sketch the function from Question 2 on the grid below. 0.75 05 0.25 1600 1800 2000 2200 2400 -0.25 -0.5 -0.75 Year TIPS4RM: MHF4U - Performance Task 2008 32 7.2.2: The Power of Nature (continued 4. Using the graph and graphing technology to assist you, determine the key features of this function including: End Behaviour Domain and Range: Extremes: Intervals of Increase and Decrease: 5. a) Find the rate of change of the function you found in Question 2 numerically and graphically at the date by which the concentration of carbon dioxide will reach 450 ppm. A graph of the region around 1= 2030 has been provided below. 0.1 0.02 2000 2002 2006 2040 004 b) Explain the meaning of the rate of change within the context of the problem. TIPSARM MHF4U - Performance Task 2008 7.2.2: The Power of Nature (continued) 6. The graphical, numeric, and algebraic models of carbon dioxide emissions vs. energy produced from wind and solar resources are provided below. 400 CO, Emissions (ppm) 395 385 380 Solar and Wind Energy Produced (MW 133.475 162.663 214.696 306.039 415.32 591.164 781.29 1008.693 1270.033 1578.153 1911.849 375 363.3475 366.295 368.24 369.34 370.92 372.9125 375.6125 379.8808 379.512 382.21 383.84 CO2 emissions (ppm) 370 365 355 350 500 1000 1500 2000 2500 Solar and Wind Energy Produced (MW) C(7) = 29.9329logr+284.5044 where is the CO2 emissions and r is the amount of solar and wind energy produced. If we continue to produce wind and solar energy according to the models given, when will the Earth reach its sustainable CO2 threshold? TIPSARM MHF4U - Performance Task 2008 7.2.2: The Power of Nature Over the past ten years the use of renewable sources of energy has become more popular. Both solar and wind energy are becoming more globally accepted as new sources of energy Below is data on annual world wind energy production and world photovoltaic production (solar energy) from 1997 and data on atmospheric Co. emissions from 1997 Wind Power Global Wind Power Production 100 Year Production (MW) 1997 7.475 80 1998 9.663 70 1999 13.696 2000 18.039 2001 24.32 2002 31.164 2003 39.29 2004 47.693 2005 59.033 2006 74.153 1990 2006 2007 93.849 Year http://www.wwindea.org home/index.php W()= 0.0612361 - 367.0021 +733178.31 - 488238151 60 Production (MW) 50 40 30 20 10 2000 2004 Global Solar Power Production 1800 1600 1400 1200 Solar Power Year Production (MW) 1997 126 1998 153 1999 201 2000 288 2001 391 2002 560 2003 742 2004 961 2005 1211 2006 1504 2007 1818 Production (MW) 1000 800 600 400 200 1998 2000 2004 2008 2002 Year http://www.carth-policy.org/Indicators/2004/indicator12_data.htm $(1) - 16.7821 -67026.31 +66924727 TIPS4RM: MHF4U - Performance Task 2008 7.2.2: The Power of Nature (continued) CO, Emissions over Time COEmissions Mean CO2 Year Emissions (ppm) 1997 363.35 1998 366.29 1999 368.24 2000 369.34 2001 370.92 2002 372.91 2003 375.61 2004 379.88 2005 379.51 2006 382.21 2007 383.84 375 - Mean CO, Emissions (ppm) 370- 365 380 355- 1998 2000 2004 2006 2002 Year CO, (1) = 0.0091465r? 34.57077 +32923 TIPSARM: MHF4U -Performance Task 2008 31 7.2.2: The Power of Nature (continued) 1. You determined the date 2030 is when the concentration of carbon dioxide will reach 450 ppm. How much total energy from renewable resources (solar and wind energy) will be produced at that time? 2. Using the three given functions for Wind Power, Solar Power and CO, Emissions, determine a combination of those functions that will model the rate at which CO2 emissions are changing with respect to total energy produced from wind and solar power. (Do not simplify the expression.) 3. Use graphing technology to sketch the function from Question 2 on the grid below. 0.75 05 0.25 1600 1800 2000 2200 2400 -0.25 -0.5 -0.75 Year TIPS4RM: MHF4U - Performance Task 2008 32 7.2.2: The Power of Nature (continued 4. Using the graph and graphing technology to assist you, determine the key features of this function including: End Behaviour Domain and Range: Extremes: Intervals of Increase and Decrease: 5. a) Find the rate of change of the function you found in Question 2 numerically and graphically at the date by which the concentration of carbon dioxide will reach 450 ppm. A graph of the region around 1= 2030 has been provided below. 0.1 0.02 2000 2002 2006 2040 004 b) Explain the meaning of the rate of change within the context of the problem. TIPSARM MHF4U - Performance Task 2008 7.2.2: The Power of Nature (continued) 6. The graphical, numeric, and algebraic models of carbon dioxide emissions vs. energy produced from wind and solar resources are provided below. 400 CO, Emissions (ppm) 395 385 380 Solar and Wind Energy Produced (MW 133.475 162.663 214.696 306.039 415.32 591.164 781.29 1008.693 1270.033 1578.153 1911.849 375 363.3475 366.295 368.24 369.34 370.92 372.9125 375.6125 379.8808 379.512 382.21 383.84 CO2 emissions (ppm) 370 365 355 350 500 1000 1500 2000 2500 Solar and Wind Energy Produced (MW) C(7) = 29.9329logr+284.5044 where is the CO2 emissions and r is the amount of solar and wind energy produced. If we continue to produce wind and solar energy according to the models given, when will the Earth reach its sustainable CO2 threshold? TIPSARM MHF4U - Performance Task 2008