## Real World Applications – Algebra I

### Topic

Carbon Dioxide Emissions in Nicaragua!

### Student Exploration

Carbon dioxide emissions are calculated by determining how much human activity has occurred. Data is gathered from fossil fuel combustion, cement manufacturing and gas flaring. The link below represents the carbon dioxide emissions in both graph form and table form.

http://rainforests.mongabay.com/carbon-emissions/nicaragua.html

Looking at this graph, we can start to predict the carbon dioxide emissions for the future using Algebra. I will make a simplified table and find a line of best fit using my graphing calculator.

For the sake of this activity, I’m going to look at the following data points:

Year | 1993 | 1997 | 2000 | 2003 | 2006 |
---|---|---|---|---|---|

Carbon emissions | 628 | 855 | 1048 | 1180 | 1182 |

You can look here to learn how to insert and plot all of these data points into your TI-83 calculator: cstl-csm.semo.edu/tansil/134/Handouts/bestfit.pdf

After entering all of the data into the graphing calculator and following all of the steps to find the line of best fit, we have \begin{align*}y = 45.23x - 89471.50\end{align*}. What does this equation mean?

Well, the \begin{align*}y-\end{align*}intercept doesn’t mean much in this case, but the slope means a lot! The rate of change, or 45.23, means that this is the amount of carbon emissions in metric tons per year.

We can also use this data to predict the carbon emissions for this year. This is the extrapolation method. Just substitute this year into the equation and solve for \begin{align*}y\end{align*}. What did you get?

For 2012, there will be 1,530 metric tons of carbon emissions. Does this answer make sense, when looking at all of your data points? Why or why not? Could there be more than one prediction for any given year?

Now, let’s look at two specific data points from the website for two different dates – 1999 and 2000. (1999, 989) and (2000, 1048). Let’s use the method of interpolation to get an idea of what the carbon emission was in September of the year 1999. Since we have two data points, we find the slope, which is \begin{align*}\frac{(1048 - 989)}{(2000 - 1999)}\end{align*}, or 59. Substituting one point and the slope into the equation, we have:

\begin{align*}Y &= mx + b\\ 989 &= 59(1999) + b\\ - 116,952 &=b \end{align*}

Our equation is \begin{align*}y = 59x - 116952\end{align*}

To find out the carbon emissions in September of 1999, we use the fact that September is 9 months into a 12 month period, or 75% into the year. We will now use 1999.75 as our \begin{align*}x\end{align*} value to find our \begin{align*}y\end{align*} value.

\begin{align*}y &= 59(1999.75) - 116952\\ y &= 1033.25\end{align*}

This makes sense, since 1033.25 is between 989 and 1048.

How does this information impact your carbon footprint? What could you do to minimize your own carbon footprint?

### Extension Investigation

On this website, see if you can recreate a similar equation and estimate what the carbon dioxide emission would be today.

http://rainforests.mongabay.com/carbon-emissions/

### Resources Cited

http://rainforests.mongabay.com/carbon-emissions/nicaragua.html

cstl-csm.semo.edu/tansil/134/Handouts/bestfit.pdf