I have attached my answer to be compared with the 2 subparts. D and Ed) Compare the predicted change in greenhouse gas emissions between 2020 and 2025 to the change between 2025 and 2030? During which five-year period is the predicted change greater and by how much or is it the same in the two-time periods?e) During what year does this function rule predict that the US emission of greenhouse gasses will decrease to 1000 million metric tons of carbon dioxide equivalents? U.S. Greenhouse Gas Emissions by Economic Sector,1990-20198.0006,c004,0002,0001990199520002005201020152019YearTransportationElectricity generationIndustryAgricultureCommercialResidentialUS. territoriesSource. U.S. EWa Invertory of US. Greenheune G Emaoro and Sinks. 1900-2019.htps www.epa.pov/gtomsomireniery-n-greeshouie-gis-emissisra-and-airksEmissions (million metric tons ofcarbon diaxide equivalent) Part 2: Exponential change modela) Find the function rule for an exponential function E(t) where t is the number of years since 2019and E(t) is the total greenhouse gasses emitted by the US. Your function should contain the points (0,6558) and (11, 3711).Let the decay function be defined as E(t)=ab^t, where aa is the gas emitted when t=0t=0 andb is thedecay factor.The graph of this function passes through the points (0, 6558), (11, 3711).Hence, it can be written that E (0) =6558 and E (11) = 3711.Solve the equation, E (0) =6558 to calculate the value of a.E (0) = 6558ab0=6558a=6558Solve the equation, E (11) =3711 to calculate the value of b.E(D) =37116558b^11=3711B^11=3711 / 6558b= (1237 / 2186) t/11= (0.5659) t/11Hence, the function is E(t)=6558(0.5659) ^ t/11, where ț is the number of years since 2019.b) Find the decay rate for this exponential function and write a sentence that describes what it tells usabout the change in greenhouse gasses under this scenario.The decay factor, b= (0.5659)b=D0.5659^111. It is known that b=1-r, where r is the decay rate.Calculate r as follows.b= (0.5659) 1/11* 0. 94961=r*0 9496R~1-0.9496= 0. 0504..= 5.04%Hence, the decay rate is about 5.04%. It implies that the rate of emission is decreasing at the rate ofabout 5.04%.c) What greenhouse gas emissions does this function predict for 2020 and for 2025?For the year 2020. the value of t is 2020 - 2019 = 1. Substitute / = 1 in the equation,E(0) = 6558(0. 5659) t/11 to calculate E (1).E (0) =6558(0. 5659) t/11E(1) =6558(0. 5659) t/11= 6227. 2056Hence, the emission is about 6227.2056 million metric tons for the year 2020.

We are given the following data. By the part (a), we get the rule for an exponential function E(t)…

Compare the predicted change in greenhouse gas emissions between 2020 and 2025 to the change between 2025 and 2030? During which five-year period is the predicted change greater and by how much or is it the same in the two-time periods? e) During what year does this function rule predict that the US emission of greenhouse gasses will decrease to 1000 million metric tons of carbon dioxide equivalents?

Compare the predicted change in greenhouse gas emissions between 2020 and 2025 to the change between 2025 and 2030? During which five-year period is the predicted change greater and by how much or is it the same in the two-time periods? e) During what year does this function rule predict that the US emission of greenhouse gasses will decrease to 1000 million metric tons of carbon dioxide equivalents?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

I have attached my answer to be compared with the 2 subparts. D and E

d) Compare the predicted change in greenhouse gas emissions between 2020 and 2025 to the change between 2025 and 2030? During which five-year period is the predicted change greater and by how much or is it the same in the two-time periods?

e) During what year does this function rule predict that the US emission of greenhouse gasses will decrease to 1000 million metric tons of carbon dioxide equivalents?

U.S. Greenhouse Gas Emissions by Economic Sector,
1990-2019
8.000
6,c00
4,000
2,000
1990
1995
2000
2005
2010
2015
2019
Year
Transportation
Electricity generation
Industry
Agriculture
Commercial
Residential
US. territories
Source. U.S. EWa Invertory of US. Greenheune G Emaoro and Sinks. 1900-2019.
htps www.epa.pov/gtomsomireniery-n-greeshouie-gis-emissisra-and-airks
Emissions (million metric tons of
carbon diaxide equivalent)

Part 2: Exponential change model
a) Find the function rule for an exponential function E(t) where t is the number of years since 2019
and E(t) is the total greenhouse gasses emitted by the US. Your function should contain the points (0,
6558) and (11, 3711).
Let the decay function be defined as E(t)=ab^t, where aa is the gas emitted when t=0t=0 andb is the
decay factor.
The graph of this function passes through the points (0, 6558), (11, 3711).
Hence, it can be written that E (0) =6558 and E (11) = 3711.
Solve the equation, E (0) =6558 to calculate the value of a.
E (0) = 6558
ab0=6558
a=6558
Solve the equation, E (11) =3711 to calculate the value of b.
E(D) =3711
6558b^11=3711
B^11=3711 / 6558
b= (1237 / 2186) t/11
= (0.5659) t/11
Hence, the function is E(t)=6558(0.5659) ^ t/11, where ț is the number of years since 2019.
b) Find the decay rate for this exponential function and write a sentence that describes what it tells us
about the change in greenhouse gasses under this scenario.
The decay factor, b= (0.5659)b=D0.5659^111. It is known that b=1-r, where r is the decay rate.
Calculate r as follows.
b= (0.5659) 1/11
* 0. 9496
1=r*0 9496
R~1-0.9496
= 0. 0504
..
= 5.04%
Hence, the decay rate is about 5.04%. It implies that the rate of emission is decreasing at the rate of
about 5.04%.
c) What greenhouse gas emissions does this function predict for 2020 and for 2025?
For the year 2020. the value of t is 2020 - 2019 = 1. Substitute / = 1 in the equation,
E(0) = 6558(0. 5659) t/11 to calculate E (1).
E (0) =6558(0. 5659) t/11
E(1) =6558(0. 5659) t/11
= 6227. 2056
Hence, the emission is about 6227.2056 million metric tons for the year 2020.

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