2.11 Quadratic Regression
Algebra 3-4
Name ________________________
Period ______
1. Individual’s Retirement Fund The following table gives the average amount,
in in thousands of dollars, of an individual’s retirement fund.
Year
1985
1990
1995
2000
2005
Value
9
19
45
101
196
a. Use this information to construct a quadratic regression to represent the model. Use
x = 1 for 1985 and x = 2 for 1986,…..
b. To the nearest thousand dollars, what will the fund be worth in 2010?
2. Average Cost of an SUV
a. Construct the quadratic regression equation to represent this model.
Year
1991
1994
1997
2000
2003
Value
$12,800
$15,500
$19,200
$24,300
$30,100
b. Using the regression model, estimate during which year would the average cost of
a new SUV reached $38,000.
3. Running. The table shows how wind affects a runner’s performance in the 200 meter dash. Postivie wind
speeds correspond to tailwinds and negative wind speeds correspond to headwinds.
Wind
Change
The change t in finishing time is the difference between the runner’s time when the
speed in
wind speed is s and the runner’s time when there is no wind. Use the calculator to
(m/sec) finishing find the best-fitting quadratic model.
a. Write the equation.
time
-6
-4
-2
0
2
4
6
(sec)
2.28
1.42
.67
0
-.057
-1.05
-1.42
b. Predict the change in finishing time when the wind speed is 10m/sec.
4. The concentration of a medication in a patient’s blood as time passes is given by the following table”
Time
(hours)
0
.5
1
1.5
2
2.5
Concentration
(mg/l)
0
78.1
99.8
84.4
50.1
15.6
a. What is the equation?
b. What is the concentration of medicine in the blood after 4 hours have
passed?
5 The number of Americans, in thousands, who are expected to be over a 100 years old .
Year
1994
1996
1998
2000
2002
2004
Number
(thousands)
50
56
65
75
94
110
a. What is the equation?
b. How many Americans are expected to be over 100 years old in the year
2010.
6. The tuition costs per quarter for taking 15 credits at a community college.
Year
1980
1983
1986
1989
1992
1995
1998
2001
2004
Need help?
Cost
$102
$173
$233
$274
$333
$450
$505
$581
$771
a. Use your calculator to find a quadratic regression for the data. What is the
quadratic function of best fit?
b. What do you think the cost will be in 2010?