example 6
Personal Savings
Using data from 1960 to 2006, the personal savings rate (as a percent) of Americans can
be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960. (Source: U.S. Census Bureau)
a. Choose an appropriate window and graph the function with a graphing calculator.
b. Use the model to estimate the personal savings rate in 2006. Is this possible?
c. Use the graph to estimate the year in which the personal savings rate is a maximum.
Chapter 1.2
2009 PBLPathways
Using data from 1960 to 2006, the personal
savings rate (as a percent) of Americans
can be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960.
a. Choose an appropriate window and
graph the function with a graphing
calculator.
Input the function
1. Press the
key below the screen.
2. Position the cursor on \Y1 =.
3. Press
.
2009 PBLPathways
Using data from 1960 to 2006, the personal
savings rate (as a percent) of Americans
can be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960.
a. Choose an appropriate window and
graph the function with a graphing
calculator.
Determine the window
4. Press
.
5. Set TblStart=0 and Tbl=5. This
will start the table at x = 0 and create
values in increments of 5.
6. Set Indpnt and Depend to Auto so
that values will be found
automatically. Press
.
2009 PBLPathways
Using data from 1960 to 2006, the personal
savings rate (as a percent) of Americans
can be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960.
a. Choose an appropriate window and
graph the function with a graphing
calculator.
Set the window
7. Press
.
8. Set Xmin=0, Xmax=50, and
Xscl=10.
9. Also set Ymin=-2, Ymax=10 and
Yscl=1.
2009 PBLPathways
Using data from 1960 to 2006, the personal
savings rate (as a percent) of Americans
can be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960.
a. Choose an appropriate window and
graph the function with a graphing
calculator.
Graph the function
10. To see the function, press
.
2009 PBLPathways
Using data from 1960 to 2006, the personal
savings rate (as a percent) of Americans
can be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960.
b. Use the model to estimate the personal
savings rate in 2006. Is this possible?
Evaluate the function
11. To find a value on this function, press
.
12. To find the value of the function in
2006, press
.
2009 PBLPathways
Using data from 1960 to 2006, the personal
savings rate (as a percent) of Americans
can be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960.
c. Use the graph to estimate the year in
which the personal savings rate is a
maximum.
Find the maximum
13. Press
to access the CALC menu.
14. Use to scroll down to maximum or
press .
2009 PBLPathways
Using data from 1960 to 2006, the personal
savings rate (as a percent) of Americans
can be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960.
c. Use the graph to estimate the year in
which the personal savings rate is a
maximum.
15. Use  to move the cursor to a point
on the left of the maximum. Press .
This is the left bound of where the
calculator will look for the maximum.
16. Use  to move the cursor to a point on
the right of the maximum. Press .
This is the right bound of where the
calculator will look for the maximum.
2009 PBLPathways
Using data from 1960 to 2006, the personal
savings rate (as a percent) of Americans
can be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960.
c. Use the graph to estimate the year in
which the personal savings rate is a
maximum.
17. Use  to move the cursor to a point
near the maximum. Press . This is
where the calculator will begin to look
for the maximum.
2009 PBLPathways
Using data from 1960 to 2006, the personal
savings rate (as a percent) of Americans
can be modeled by the function
y  0.00796 x 2  0.205 x  7.044
where x is the number of years after 1960.
c. Use the graph to estimate the year in
which the personal savings rate is a
maximum.
17. Use  to move the cursor to a point
near the maximum. Press . This is
where the calculator will begin to look
for the maximum.
This indicates that the maximum occurred
approximately 12.9 years after 1960 or in
1972. The maximum personal savings
rate was about 8.4%.
2009 PBLPathways