Investigation 2: The Greenhouse Effect and Carbon Dioxide

I'm sure you've heard recent reports about global warming.

Let's examine the issue a little closer and use a linear

function to make some predictions about the future

of this phenomenon.

Global warming is the steady increase in the average

temperature of the Earth's near-surface air and oceans in

recent decades.

It is caused by the emission of gases that trap the sun's

heat in the Earth's atmosphere.

Closely related is the natural process called

the greenhouse effect.

The various gases in the atmosphere absorb the heat

lost by the Earth at night and radiate it back for the

survival of life on Earth.

The problem though is that one of these gases

carbon dioxide

is on the rise.

Since it is primarily the product of fossil fuel

combustion, such as gasoline and coal, many people believe

its increase is the result of pollution.

The concern is that higher global temperatures entail

weather-related disasters such as heat waves, droughts,

floods, hurricanes, and more.

Global levels of carbon dioxide, or CO2, began an

upward spike around 1960.

This table shows approximate CO2 levels in the Earth's

atmosphere in 1960 and in 2007.

CO2 is measured in parts per million, or PPM.

So for example, 380 PPM means that there are 380 molecules

of CO2 for every million molecules of dry air.

Since CO2 levels have risen steadily from 1960 onwards,

we'll set 1960 as our starting point, x equals 0, and assume

linear growth from then on.

Let's find a linear equation for CO2 levels, y, as a

function of the year, x.

First, calculate the slope using the slope formula and

the two given points.

Then use the slope-intercept form, y equals mx plus b,

since the y-intercept is given.

The y-intercept is the y-value when x equals 0.

The slope m equals 380 minus 318 over 47 minus 0.

Or, 62 divided by 47, which is approximately 1.32.

So the linear equation y equals 1.32x plus 318 gives

the global level of CO2 for any year x since 1960.

To predict the amount of carbon dioxide in the Earth's

atmosphere in the year 2025, assuming the constant rise

will continue, you would set x equal to 65, because 2025 is

65 years after 1960, and obtain y equals 1.32

times 55 plus 318.

Equals 85.8 plus 318, which is 403.8 parts per million.

A very alarming level indeed.

As a final exercise, let's use a powerful feature of the

TI-Nspire called linear regression to predict CO2

levels in 2025 and 2050 based on the following data.

The TI-Nspire finds the line that would

best fit these points.

It's called the line of best fit.

Turn on the TI-Nspire.

Press the Home key to open a new document.

Choose whether or not to save your open document.

Then start the list and spreadsheet application.

Enter the years in column A, pressing

Enter after each entry.

When you're done, use the nav pad to move to column B, where

you'll enter the CO2 level.

Pause the video to enter your data.

Press the Up Arrow once more to select column B. It should

now be highlighted.

Then press and hold the Shift key while

pressing the Left Arrow.

Now both columns should be selected.

Next, press Menu, 4, 1, and 3 to select Linear Regression.

Press Tab to move all the way down to OK and

press Enter, or click.

Your cursor lands on entry 1 of column D.

To widen the column, press Menu, 1, 2, and 1, followed by

the Right Arrow a few times until the width is

satisfactory.

Then press Enter.

Notice in this column that the slope m is pretty close to

what we found with just two points.

And the coefficients, r square and r below it, are both very

close to 1, which would represent a perfect fit.

To plot the six data points and the regression line

together, press Control and I, then 2 to

insert a new graph page.

Press Menu, 3, and 4 for a scatter plot.

Press the Down Arrow to select stat.xreg.

Press on the Click button.

Next, select stat.yreg.

So let's zoom data by pressing Menu, 4, and 9.

To plot the regression line over the points, press

Menu, 3, and 1.

Press the Up Arrow to access f1.

And finally, press Enter.

Lastly, press Control-T for the function table and Menu,

5, and 5 to change the table start value to 2025.

Tab down to select OK.

You can see that in 2025, the CO2 levels will be about 402

PPM, very close to what we found.

Use the nav pad to scroll down to 2050 and find 435.085 PPM.

We'll need to find creative ways to limit greenhouse gases

if we want future generations to live in harmony with the

environment.

In closing, let's summarize the meaning of a linear

relationship between two variables, x and y.

Geometrically, it means the graph is a straight line.

Algebraically, it means the exponents of x and y are both

equal to 1.

And mathematically, it means that y increases

or decreases

proportionally with x.

I hope you'll investigate linear relationships further

on your own.

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