Download 3.2 Finding Power Equations

3.2 Finding Power Equations
“x” cannot equal zero
Remember, the format of a power equation is y  ax
Previously, when we had a table of data we could use
different values to represent the years (like: let 1990 be
year 0). For power equations to work, you can’t do this.
The equation will “fail.” Instead, we take the first year
and set it equal to a different number (like maybe 10).
b
Make sure you read your test to get more of an explanation here.
Debt
(thousands)
2010
$39.88
1. The American debt per capita is shown in the chart. This is the total
2011
$45.09
debt divided among every man, woman and child in America …
2012
$48.60
2013
$52.09
wow!
2014
$52.69
a) Consider 2009 to be year 0 and use regression to find a power equation to model the data.
Round the numbers in your equation to 2 decimal
places.
b) Use your equation to predict the debt in 2016.
Practice
Year
Solutions:
a)
Adding a column to the table will help with the data entry. Enter
into the calculator the data from the table, then select the power option
to generate the regression equation:
0.18
y  39.897 x
Years
Since
2009
Year
Debt
(thousands)
1
2
3
4
5
2010
2011
2012
2013
2014
$39.88
$45.09
$48.60
$52.09
$52.69
b)
2016  2009  7
Using the equation from a),
substitute 7 for x and solve for y.
y  39.897  70.18
y  56.631
y  $56, 631 9.
Practice
Since we now have quadratic and
power models that both accommodate curved data,
reconsider the previous question.
a) Notice the power curve in the previous question is not a
great fit to the data (compare the fit of a quadratic curve
below to the power function in the previous problem).
Use regression to find a
quadratic equation to
model the data. Round
the numbers in your
equation to 3 decimal
places.
b) Use your equation to
make a better prediction
for the PCB
concentration that you
could expect in a 10 year
old trout, round to the
nearest tenth.
Solutions:
a)
Enter into the calculator the data from the table, then select the quad option to generate the
regression equation:
y  0.130 x 2  0.351x  0.599
b)
Using the equation from a), substitute 10 for x and solve for y.
y  0.130 102  0.351 10  0.599
y  17.1 ppm
Homework: 3, 7, 10, 11