Algebra Applications: Drilling for Oil

[Music]

The Arctic National Wildlife Reserve, ANWR, is in

a corner of Alaska.

It is a national park the size of South Carolina.

It is a vast area with rivers, mountains, and wildlife.

Large herds of porcupine caribou roam the valleys.

Polar bears search for food, and in the spring flowers and

birds make their brief appearance.

But this national park is also a national treasure.

Geologists estimate that there could be as much as fifteen

billion barrels of oil in the coastal region.

This should not be too surprising since Prudhoe Bay,

North America's largest source of oil, is a few miles down

the coast.

How long will fifteen billion barrels of oil last?

At one million barrels a day, and using scientific notation,

we get one point five ten to he fourth days.

Converting that to years we find that there is enough oil

for approximately forty-one years.

But how does this compare to our current usage of oil?

The US currently uses twenty-one million barrels of

oil per day.

So an additional one million barrels represents

five percent.

This is not a huge amount, but here is where ANWR can make a

big difference, and for that we'll need the TI-Nspire.

For this activity you will be graphing data for the daily US

consumption of oil from 1980 to 2007.

Turn on the TI-Nspire.

Create a new document.

You may need to say a previous document.

Create a new list and spreadsheet window.

Enter the years in column A, pressing ENTER after

each entry.

When you're done move to column B where you'll enter

the daily oil usage data.

The usage data is in thousands of barrels, so each number of

the second column represents millions of barrels.

Pause the video to enter your data.

Be sure to include the column headings for each data set and

make a note of these column headings.

We want to test if this data set is linear.

To do that we perform a linear regression, which is a way of

testing to see how closely the graph of the data aligns with

the linear function.

Before performing a linear regression you must select

the data.

Move the cursor to the top of column B.

Beside the letter B, press the UP ARROW once more to select

the column.

It should now be highlighted.

Then press and hold the SHIFT key while holding the

LEFT ARROW.

Now both columns should be selected.

Next press MENU, and under statistics select STAT

CALCULATIONS, and under that select LINEAR REGRESSION.

Press tab to move all the way down to OK and press ENTER,

or click.

Your cursor lands on entry one of column D.

To widen the column press MENU, and under ACTION select

RESIZE, and under that MENU select RESIZE COLUMN followed

by the RIGHT ARROW a few times until the width

is satisfactory.

Then press ENTER.

Notice the coefficients r2 and r are both very close to

1, which would represent a good fit.

To plot the data points and their regression line together

press CONTROL and I and select GRAPHS to insert a new

graph page.

Press MENU, and under GRAPH TYPE select SCATTER PLOT.

Input the name of the column heading of column A in your

spreadsheet, press the DOWN ARROW, then input the name

of the column heading of column B in your spreadsheet.

Press ENTER again.

To see the data press MENU, and under ZOOM, select

ZOOM DATA.

To plot the regression line over the points press MENU,

and under GRAPH TYPES select FUNCTION.

Press the UP ARROW to access F1, and finally press ENTER.

Lastly, press control and T for the function table.

Press MENU, and under tables select edit table settings.

Change the table start value to 1980.

Tab down to select OK.

Suppose that ANWR oil production started in 2010 and

took five years before the oil became available.

By 2015 the expected increase in demand from 2007 is what

ANWR could mostly take care of.

That, combined with more fuel efficiency would keep the US

from becoming more dependent on foreign oil supplies.

This would be a small step in the direction of reducing our

dependence on oil and looking for alternatives.

[Music]

Narrator: Everyone knows the value of exercise.

In particular aerobic exercise is great for your metabolism,

and for your heart.

Whether jogging, cycling, or swimming, aerobic exercise

exerts your heart muscle and helps your metabolism.

[Music]

Narrator: But as you get older the amount of aerobic

exercise changes.

The exertion on the heart needs to decrease with age.

For a twenty year old the maximum number of heartbeats

should not exceed two hundred beats per minute.

For a sixty year old, the maximum number of heartbeats

should not exceed one hundred sixty beats per minute.

There is a linear function that relates heartbeat to age,

y=220 - x , where y is the maximum number of

heartbeats per minute, and x is the age of the person.

Suppose that your health teacher wants you to create an

exercise chart that shows the maximum heart rate for people

aged fifteen to sixty-five.

Turn on the TI-Nspire.

Create a new document.

You may need to save a previous document.

Create a new graph window.

Input the function 220 - x and press ENTER.

Notice that there is no equation on screen.

This is because the y intercept, 220 is off the screen.

Change the WINDOW SETTINGS by pressing MENU, and under

WINDOW ZOOM select WINDOW SETTINGS.

Change x-min to 0, x-max to 70, y-min to 150, y-max to 250.

Now you can see the graph.

What we're interested in is generating a data table.

To do that click on CONTROL and T.

Change the table settings, selecting MENU, and under

TABLE select edit TABLE SETTINGS.

Change the table start value to 15 and tab your way to

the OK button and click on it.

You can now take this data table and bring it into a

spreadsheet or word processing program.

Simply highlight the data table and copy the data to

the clipboard.

Paste the data into your spreadsheet or word processing

program, format the table and print it.

You now have an aerobic exercise chart for people

from ages fifteen to sixty-five.

[Music]