# Math Help - Homework Assignment

1. ## Homework Assignment

Can someone look over the following assignment and point out what if anything i missed or got wrong

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Greenhouse Gas Emissions in Australia

Australia is a relatively small producer of greenhouse gases, accounting for approximately 1.4% of global emissions. However, its emissions per capita rank third amongst industrialized countries. This is due to particular circumstances including an abundance of fossil fuel resources, a dispersed population with a consequent heavy dependence on fossil fuel based transport, and a relatively rapid rate of population growth.

The following table gives Australia's net greenhouse gas emissions in Mt CO2-e by year. Mt is the abbreviation for megaton, which is one million tons. CO2-e represents carbon dioxide equivalent emissions. CO2 equivalent emissions are calculated by measuring the global warming potential of a greenhouse gas relative to that of CO2. For example, carbon dioxide is assigned a global warming potential (GWP) of 1 and methane a GWP of 21. That is, one ton of methane is equivalent to 21 tons of carbon dioxide in terms of its effect on global warming.

Year 1990 1991 1992 1993 1994 1995 1996
Mt CO2-e 384.9 386.1 386.9 389.6 394.2 406.8 419.3
Source: National Greenhouse Gas Inventory

Group Work

1. Make points out of the data and plot them on a (t,G) coordinate system where t represents the number of years after 1990 and G represents the Australian total greenhouse gas emissions (in Mt CO2-e) in the year 1990 + t.

On last page on graph paper

2. Find a piecewise model for the data and graph it together with the original data points. You may want to use a parabola for the points corresponding to the years 1990 - 1994 and a line corresponding to the years 1994 - 1996. Round the coefficients to three decimal places. Does the model provide a good fit for the data points? Explain.

0.506X^2+0.345X+384.956=Y

3. Use the model to predict Australia's total greenhouse gas emissions in 2000. In 2010.

Gas Emissions in 2000 Gas Emissions in 2010

G=5.733*10+384.9 G=5.733*20+384.9

=442.23 =499.56

4. According to the model, what is the predicted percentage increase in Australia's total emissions between 1990 and 2000? Between 1990 and 2010?

442.233-384.9

--------- = .1489555729 = 14.89%
384.9

5. The Australian government predicts that Australia's greenhouse gas emissions would be approximately 552 Mt CO2-e in 2010, a 43% increase over 1990 levels, if no measures were taken to reduce emissions. Do these predictions agree with those found using your model? Explain.

No these predictions do not agree with those I found using the model. The reason they do not agree is because the model is an approximation not exact

Australia took an active part in negotiating the Kyoto Protocol to the Framework Convention on Climate Change and subsequently signed the Protocol on April 29, 1998. The Kyoto Protocol is an international agreement in which developed countries collectively agreed to reduce greenhouse gas emissions by at least five percent below 1990 levels by 2008 - 2012. Within this target, individual countries have agreed to legally binding differentiated targets ranging from an 8% reduction to a 10% increase above 1990 levels by 2008 - 2012. Australia's differentiated target is an eight-percent increase above 1990 levels by 2010. Suppose that Australia implements a plan for reducing greenhouse gas emissions by a straight line decrease beginning in the year 2000.

6. Determine Australia's target emissions under the Kyoto Protocol.

384.9*1.08

=415.692

7. Use your answer to exercise 3 to determine how much the emissions must decrease each year to reach the desired level?

499.56-442.23=57.33

57.33/10

Each year emissions must decrease 5.733 to reach the target goal in 2010

8. Write a linear equation that defines Australia's target greenhouse gas emissions each year from 2000 through 2010. Call this function TGE(t). (Remember t = 0 in 1990.)

G = mt+b
G=gas
M= -2.654
T= years after 2000
B= 442.233

G=-2.654*t+442.233

9. Graph your target emission function and your original greenhouse gas emissions function on the same coordinate system for the years 2000 through 2010.

On last page on graph paper

2. Look at question 2:

Originally Posted by vincentharris
2. Find a piecewise model for the data and graph it together with the original data points. You may want to use a parabola for the points corresponding to the years 1990 - 1994 and a line corresponding to the years 1994 - 1996. Round the coefficients to three decimal places. Does the model provide a good fit for the data points? Explain.

0.506X^2+0.345X+384.956=Y
You are asked for a piecewise model, and strongly nudged in
the direction of having two pieces one parabolic covering 1990-1994,
and the second linear covering 1994-1996.

This would look something like:

$y\ =\ a.x^2\ +\ b.x\ +\ c\ \mbox{, for}\ 1990\ \leq\ y\ \leq\ 1994$

$y\ =\ d.x\ +\ e\ \mbox{, for}\ 1994\ \leq\ y\ \leq\ 1996$

where $a,\ b,\ c,\ d,\ e$ are to be determined from the
data, and the two pieces should give the same result for 1994.

RonL

3. that makes sense, thank you

besides that for other problems posted do you see anything wrong?

4. Originally Posted by vincentharris
that makes sense, thank you

besides that for other problems posted do you see anything wrong?
Not in principle, but the actual numerical values for all
the subsequent parts which depend on part 2 will
change if you alter the answer to part 2.

RonL