7. Salmon Survival For reasons that are not yet fully understood, the number of fingerling salmon that survive the trip from their riverbed spawning grounds to the open ocean varies approximately sinusoidally from year to year. The table shows the number of salmon that hatch in a certain British Columbia creek and then make their way to the Strait of Georgia The data are given in thousands of fingerlings. over a period of 16 years. (a) Make a scatter plot of the data. (b) Find a sine curve that models the data (as in Example 1). (c) Graph the function you found in part (b) together with the scatter plot. (d) Use a graphing calculator to find the sine curve that best fits the data (as in Example 2). Compare to your answer from part (b). Year Salmon (x 1000) Year Salmon (× 1000) 1985 43 1993 56 1986 36 1994 63 1987 27 1995 57 1988 23 1996 50 1989 26 1997 44 1990 33 1998 38 1991 43 1999 30 1992 50 2000 22
7. Salmon Survival For reasons that are not yet fully understood, the number of fingerling salmon that survive the trip from their riverbed spawning grounds to the open ocean varies approximately sinusoidally from year to year. The table shows the number of salmon that hatch in a certain British Columbia creek and then make their way to the Strait of Georgia The data are given in thousands of fingerlings. over a period of 16 years. (a) Make a scatter plot of the data. (b) Find a sine curve that models the data (as in Example 1). (c) Graph the function you found in part (b) together with the scatter plot. (d) Use a graphing calculator to find the sine curve that best fits the data (as in Example 2). Compare to your answer from part (b). Year Salmon (x 1000) Year Salmon (× 1000) 1985 43 1993 56 1986 36 1994 63 1987 27 1995 57 1988 23 1996 50 1989 26 1997 44 1990 33 1998 38 1991 43 1999 30 1992 50 2000 22
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
Related questions
Question
Number 7
![6. Predator Population When two species interact in a predator/prey relationship, the
populations of both species tend to vary in a sinusoidal fashion. (See Discovery Project
Predator/Prey Models referenced on page 529). In a certain midwestern county, the main
food source for barn owls consists of field mice and other small mammals. The table oiv
the population of barn owls in this county every July I over a 12-year period.
tion
(a) Make a scatter plot of the data.
(b) Find a sine curve that models the data (as in Example 1).
(c) Graph the function you found in part (b) together with the scatter plot.
(d) Use a graphing caleulator to find the sine curve that best fits the data (as in
Example 2). Compare to your answer from part (b).
7. Salmon Survival For reasons that are not yet fully understood, the number of fingerling
salmon that survive the trip from their riverbed spawning grounds to the open ocean varies
approximately sinusoidally from year to year. The table shows the number of salmon that
hatch in a certain British Columbia creek and then make their way to the Strait of Georgia.
The data are given in thousands of fingerlings. over a period of 16 years.
(a) Make a scatter plot of the data.
(b) Find a sine curve that models the data (as in Example 1),
(c) Graph the function you found in part (b) together with the scatter plot.
(d) Use a graphing calculator to find the sine curve that best fits the data (as in
Example 2). Compare to your answer from part (b).
Year
Salmon (x 1000)
Year
Salmon (x 1000)
1985
43
1993
56
1986
36
1994
63
1987
27
1995
57
1988
23
1996
50
1989
26
1997
44
1990
33
1998
38
1991
43
1999
30
1992
50
2000
22
8. Sunspot Activity Sunspots are relatively "cool" regions on the sun that appear as dark
spots when observed through special solar filters. The number of sunspots varies in an
11-year cycle. The table gives the average daily sunspot count for the years 1968–2012.
(a) Make a scatter plot of the data.
(b) Find a cósine curve that models the data (as in Example 1).
(c) Graph the function you found in part (b) together with the scatter plot.
(d) Use a graphing calculator to find the sine curve that best fits the data (as in Exam-
ple 2). Compare to your answer in part (b).
Year
Sunspots
Year
Sunspots
Year
Sunspots
Year
Sunspots
1968
106
1980
154
1991
1969
105
1981
145
2002
104
140
1992
1970
104
1982
115
94
2003
63
1993
1971
67
54
1983
66
1994
2004
40
1972
69
1984
45
29
2005
30
1995
1973
38
17
1985
1986
17
1996
2006
15
1974
34
8.
13
1997
2007
1975
15
1987
29
21
2008
3.
1076
1998
12
IORN
64
I00
2009
3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F890df8a5-1929-4d4b-b946-431771941a1a%2F32731e5c-415e-4631-90f6-43be9cd3038d%2Fbotxmf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:6. Predator Population When two species interact in a predator/prey relationship, the
populations of both species tend to vary in a sinusoidal fashion. (See Discovery Project
Predator/Prey Models referenced on page 529). In a certain midwestern county, the main
food source for barn owls consists of field mice and other small mammals. The table oiv
the population of barn owls in this county every July I over a 12-year period.
tion
(a) Make a scatter plot of the data.
(b) Find a sine curve that models the data (as in Example 1).
(c) Graph the function you found in part (b) together with the scatter plot.
(d) Use a graphing caleulator to find the sine curve that best fits the data (as in
Example 2). Compare to your answer from part (b).
7. Salmon Survival For reasons that are not yet fully understood, the number of fingerling
salmon that survive the trip from their riverbed spawning grounds to the open ocean varies
approximately sinusoidally from year to year. The table shows the number of salmon that
hatch in a certain British Columbia creek and then make their way to the Strait of Georgia.
The data are given in thousands of fingerlings. over a period of 16 years.
(a) Make a scatter plot of the data.
(b) Find a sine curve that models the data (as in Example 1),
(c) Graph the function you found in part (b) together with the scatter plot.
(d) Use a graphing calculator to find the sine curve that best fits the data (as in
Example 2). Compare to your answer from part (b).
Year
Salmon (x 1000)
Year
Salmon (x 1000)
1985
43
1993
56
1986
36
1994
63
1987
27
1995
57
1988
23
1996
50
1989
26
1997
44
1990
33
1998
38
1991
43
1999
30
1992
50
2000
22
8. Sunspot Activity Sunspots are relatively "cool" regions on the sun that appear as dark
spots when observed through special solar filters. The number of sunspots varies in an
11-year cycle. The table gives the average daily sunspot count for the years 1968–2012.
(a) Make a scatter plot of the data.
(b) Find a cósine curve that models the data (as in Example 1).
(c) Graph the function you found in part (b) together with the scatter plot.
(d) Use a graphing calculator to find the sine curve that best fits the data (as in Exam-
ple 2). Compare to your answer in part (b).
Year
Sunspots
Year
Sunspots
Year
Sunspots
Year
Sunspots
1968
106
1980
154
1991
1969
105
1981
145
2002
104
140
1992
1970
104
1982
115
94
2003
63
1993
1971
67
54
1983
66
1994
2004
40
1972
69
1984
45
29
2005
30
1995
1973
38
17
1985
1986
17
1996
2006
15
1974
34
8.
13
1997
2007
1975
15
1987
29
21
2008
3.
1076
1998
12
IORN
64
I00
2009
3.
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