Alg 1 TE Lesson 10-8

Math Tip
Exercises 19–24 Remind students
that r is the correlation coefficient.
The nearer r is to 1 or -1, the
more closely the data cluster
around the model. The closer r is
to 1 or - 1, the greater r 2 is.
Also, the TI-83 Plus does not
automatically show r-values for
regressions. This feature, under
catalog, is called DiagnosticsOn,
and needs to be highlighted and
switched on for this to happen.
pages 563–566
16a. p
602
Exercises
linear
18. Answers may vary.
Sample: Linear data
have a common first
difference, quadratic
data have a common
second difference, and
exponential data have a
common ratio.
25a. i. x y
29f.
Population
ii.
iii.
Sales (billions of dollars)
6000
4000
2000
O
1 –2
2 1
3 6
4 13
5 22
x y
1 3
2 12
3 27
4 48
5 75
x y
1 –1
2 6
3 21
4 44
5 75
y
800
700
600
500
400
300
200
100
O
t
4 8 12 16
Year
)3 )2
)5 )2
)7 )2
)9
) 9 )6
)15 )6
)21 )6
)27
) 7 )8
)15 )8
)23 )8
)31
x
5 10 15 20
Year
Age
(years)
B
Value
(dollars)
0 16,500
1 14,500
2 12,750
3 11,200
4 9900
Apply Your Skills
16c. 600, 600, 600;
120, 120, 120
Population
Year (millions)
0 4457
5 4855
10 5284
15 5691
20 6080
SOURCES: U. S. Census Bureau.
Go to www.PHSchool.com
for a data update.
Web Code: atg-9041
GO
nline
Homework Help
Visit: PHSchool.com
Web Code: ate-1008
14. Car Value The value of a car over several years is shown in the table at the left.
a. Determine which model is most appropriate for the data. exponential
b. Write an equation to model the data. y ≠ 16,500 ? 0.88 x
15. Physics Your class collected the data in the table
at the right by rolling a ball down a ramp. The
ramp had the same angle throughout. a. 41, 123, 206
a. Find the differences of consecutive terms.
b. Find the second differences. 82, 83
c. Write an equation to model the data. Let t
be the time in seconds and d be the distance
in centimeters. d ≠ 41t 2
d. Based on your equation, how far would the ball have rolled down the ramp
in 2.5 seconds? 256.25 cm
16. The table below shows the projected population of a small town. Let t = 0
correspond to the year 2020. a. See margin.
a. Graph the data. Does the graph suggest a
linear, exponential, or quadratic model?
Year Population
b. What is the difference in years? 5 years
0 5100
c. Find the differences of consecutive terms.
5 5700
Divide by the difference in years to find
10 6300
possible common differences. See left.
15 6900
d. Write a linear equation to model the data
based on your answer to part (c). p ≠ 120t ± 5100
17. Population The table at the left shows the world population in millions from
GPS 1980 to 2000. The year t = 0 corresponds to 1980.
a. What is the difference in years? 5
b. Find the differences of consecutive terms. Divide by the difference in years
to find possible common differences. 398, 429, 407, 389; 79.6, 85.8, 81.4, 77.8
c. Find the average of the common differences you found in part (b). about 81.2
d. Write a linear equation to model the data based on your answer to part (c).
e. Use your equation to predict the world population in 2010.
d. p ≠ 81.2t ± 4457 e. 6893 million, or about 6.9 billion
18. Writing Explain in writing to a classmate how to decide whether a linear,
exponential, or quadratic function is the most appropriate equation to model
a set of data. See margin.
Use LinReg, ExpReg, or QuadReg to find an equation to model the data.
The greatest value of r 2 indicates the best model for the data.
19. x y 20. x y 21. x y
0 1.7
1 1.4
2 4.7
3
y ≠ 0.875x 2 – 0.435x ± 1.515 y ≠ 1.987 ? 0.770 x y ≠ 2.125x 2 – 4.145x ± 2.955
22. x y 23. x y 24. x y
1
7.9
4.3
0 5.1
1 4.3
2 2.2
0 2.0
1 1.5
2 1.2
3
1
0 3.5
3 1.3
3 0.2
3 1.76
y ≠–0.336x 2 – 0.219x ± 4.666 y ≠–1.1x ± 3.5 y ≠ 0.102 ? 2.582 x
602 Chapter 10 Quadratic Equations and Functions
0.9
4.6
1 2.4
2 1.3
Time
(seconds)
0 0
1 41
2 164
3 370
0 2.8
1 1.4
2 2.7
3
1
Distance
(centimeters)
9.8
0.04
0 0.10
1 0.26
2 0.68