Finding the equation for a sinusoidal cycle/function given points.Pre Calc, Sinusoidal FunctionFinding the vertical shift of a sinusoidal functionFitting a sinusoidal function to three known pointsCalculating Sinusoidal Equation From Irregularly Given InformationFinding periodic (trigonometric?) function given pointsFinding the sine graph equation given pointsSinusoidal function from $4$ knownsIntuition for matrix representation of deterministic sinusoidal cycleFinding the graph of a sinusoidal functionHow to construct sinusoidal functions given two points?
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Finding the equation for a sinusoidal cycle/function given points.
Pre Calc, Sinusoidal FunctionFinding the vertical shift of a sinusoidal functionFitting a sinusoidal function to three known pointsCalculating Sinusoidal Equation From Irregularly Given InformationFinding periodic (trigonometric?) function given pointsFinding the sine graph equation given pointsSinusoidal function from $4$ knownsIntuition for matrix representation of deterministic sinusoidal cycleFinding the graph of a sinusoidal functionHow to construct sinusoidal functions given two points?
$begingroup$
We are given the population of a fictional animal at different years:
$$beginarrayl
textrmYear & textrmPopulation\hline
1945 & 347,0000\
1955 & 76,000\
1965 & 295,000\
1975 & 84,000\
1985 & 243,000\
1995 & 92,000
endarray$$
We are asked to come up with a formula for the population over time. I am so lost. I can get a graph to go through the first 2 points, or I can get it to go through all of the maximums or all of the minimums, but I can't get it to go through all of the points in one go.
algebra-precalculus functions trigonometry
edited May 17 '14 at 7:31
MattAllegro
2,58751432
asked May 15 '14 at 3:35
John SmithJohn Smith
211
$endgroup$
add a comment |
$begingroup$
We are given the population of a fictional animal at different years:
$$beginarrayl
textrmYear & textrmPopulation\hline
1945 & 347,0000\
1955 & 76,000\
1965 & 295,000\
1975 & 84,000\
1985 & 243,000\
1995 & 92,000
endarray$$
We are asked to come up with a formula for the population over time. I am so lost. I can get a graph to go through the first 2 points, or I can get it to go through all of the maximums or all of the minimums, but I can't get it to go through all of the points in one go.
algebra-precalculus functions trigonometry
edited May 17 '14 at 7:31
MattAllegro
2,58751432
asked May 15 '14 at 3:35
John SmithJohn Smith
211
$endgroup$
$begingroup$
What do you mean by fitting? @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:45
$begingroup$
We haven't really learned one that would work for this. I am currently in Algebra II Trigonometry honors. My method for attacking this was realizing that the relative maximums and minimums change by -52,000 and +8,000 respectively each 10 years. Then I tried to work that into the normal A·(sin or cos)(bx+c)+d. @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:51
add a comment |
$begingroup$
We are given the population of a fictional animal at different years:
$$beginarrayl
textrmYear & textrmPopulation\hline
1945 & 347,0000\
1955 & 76,000\
1965 & 295,000\
1975 & 84,000\
1985 & 243,000\
1995 & 92,000
endarray$$
We are asked to come up with a formula for the population over time. I am so lost. I can get a graph to go through the first 2 points, or I can get it to go through all of the maximums or all of the minimums, but I can't get it to go through all of the points in one go.
algebra-precalculus functions trigonometry
edited May 17 '14 at 7:31
MattAllegro
2,58751432
asked May 15 '14 at 3:35
John SmithJohn Smith
211
$endgroup$
We are given the population of a fictional animal at different years:
$$beginarrayl
textrmYear & textrmPopulation\hline
1945 & 347,0000\
1955 & 76,000\
1965 & 295,000\
1975 & 84,000\
1985 & 243,000\
1995 & 92,000
endarray$$
We are asked to come up with a formula for the population over time. I am so lost. I can get a graph to go through the first 2 points, or I can get it to go through all of the maximums or all of the minimums, but I can't get it to go through all of the points in one go.
algebra-precalculus functions trigonometry
algebra-precalculus functions trigonometry
edited May 17 '14 at 7:31
MattAllegro
2,58751432
asked May 15 '14 at 3:35
John SmithJohn Smith
211
edited May 17 '14 at 7:31
MattAllegro
2,58751432
asked May 15 '14 at 3:35
John SmithJohn Smith
211
edited May 17 '14 at 7:31
MattAllegro
2,58751432
edited May 17 '14 at 7:31
MattAllegro
2,58751432
edited May 17 '14 at 7:31
MattAllegro
2,58751432
2,58751432
asked May 15 '14 at 3:35
John SmithJohn Smith
211
asked May 15 '14 at 3:35
John SmithJohn Smith
211
asked May 15 '14 at 3:35
John SmithJohn Smith
211
211
$begingroup$
What do you mean by fitting? @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:45
$begingroup$
We haven't really learned one that would work for this. I am currently in Algebra II Trigonometry honors. My method for attacking this was realizing that the relative maximums and minimums change by -52,000 and +8,000 respectively each 10 years. Then I tried to work that into the normal A·(sin or cos)(bx+c)+d. @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:51
add a comment |
$begingroup$
What do you mean by fitting? @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:45
$begingroup$
We haven't really learned one that would work for this. I am currently in Algebra II Trigonometry honors. My method for attacking this was realizing that the relative maximums and minimums change by -52,000 and +8,000 respectively each 10 years. Then I tried to work that into the normal A·(sin or cos)(bx+c)+d. @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:51
$begingroup$
What do you mean by fitting? @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:45
$begingroup$
What do you mean by fitting? @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:45
$begingroup$
We haven't really learned one that would work for this. I am currently in Algebra II Trigonometry honors. My method for attacking this was realizing that the relative maximums and minimums change by -52,000 and +8,000 respectively each 10 years. Then I tried to work that into the normal A·(sin or cos)(bx+c)+d. @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:51
$begingroup$
We haven't really learned one that would work for this. I am currently in Algebra II Trigonometry honors. My method for attacking this was realizing that the relative maximums and minimums change by -52,000 and +8,000 respectively each 10 years. Then I tried to work that into the normal A·(sin or cos)(bx+c)+d. @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:51
add a comment |
1 Answer
1
active
oldest
votes
$begingroup$
On the drawing of the given data, one can see that the maximums and minimums are respectively linear functions of the years. It is easy to express both linear équations, which are significant of the evolution of the population.
Of course, it is possible to find a "damped" sinusoidal function which accurately fits the six given points (with a 10 years half-period) The coefficients $C_0, C_1, C_2, C_3$are computed thanks to linear regression. But what is the meaning of such a function ? This is questionable ! Why not a one year period, ore else ? Are you sure that the problem requires such a sinusoidal model ? If statistical computations have to be carried out, why not directly using the given data instead of an intermediate function with, may be, no real significance!
answered May 17 '14 at 10:16
JJacquelinJJacquelin
45.1k21855
$endgroup$
add a comment |
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$begingroup$
On the drawing of the given data, one can see that the maximums and minimums are respectively linear functions of the years. It is easy to express both linear équations, which are significant of the evolution of the population.
Of course, it is possible to find a "damped" sinusoidal function which accurately fits the six given points (with a 10 years half-period) The coefficients $C_0, C_1, C_2, C_3$are computed thanks to linear regression. But what is the meaning of such a function ? This is questionable ! Why not a one year period, ore else ? Are you sure that the problem requires such a sinusoidal model ? If statistical computations have to be carried out, why not directly using the given data instead of an intermediate function with, may be, no real significance!
answered May 17 '14 at 10:16
JJacquelinJJacquelin
45.1k21855
$endgroup$
add a comment |
$begingroup$
On the drawing of the given data, one can see that the maximums and minimums are respectively linear functions of the years. It is easy to express both linear équations, which are significant of the evolution of the population.
Of course, it is possible to find a "damped" sinusoidal function which accurately fits the six given points (with a 10 years half-period) The coefficients $C_0, C_1, C_2, C_3$are computed thanks to linear regression. But what is the meaning of such a function ? This is questionable ! Why not a one year period, ore else ? Are you sure that the problem requires such a sinusoidal model ? If statistical computations have to be carried out, why not directly using the given data instead of an intermediate function with, may be, no real significance!
answered May 17 '14 at 10:16
JJacquelinJJacquelin
45.1k21855
$endgroup$
add a comment |
$begingroup$
On the drawing of the given data, one can see that the maximums and minimums are respectively linear functions of the years. It is easy to express both linear équations, which are significant of the evolution of the population.
Of course, it is possible to find a "damped" sinusoidal function which accurately fits the six given points (with a 10 years half-period) The coefficients $C_0, C_1, C_2, C_3$are computed thanks to linear regression. But what is the meaning of such a function ? This is questionable ! Why not a one year period, ore else ? Are you sure that the problem requires such a sinusoidal model ? If statistical computations have to be carried out, why not directly using the given data instead of an intermediate function with, may be, no real significance!
answered May 17 '14 at 10:16
JJacquelinJJacquelin
45.1k21855
$endgroup$
On the drawing of the given data, one can see that the maximums and minimums are respectively linear functions of the years. It is easy to express both linear équations, which are significant of the evolution of the population.
Of course, it is possible to find a "damped" sinusoidal function which accurately fits the six given points (with a 10 years half-period) The coefficients $C_0, C_1, C_2, C_3$are computed thanks to linear regression. But what is the meaning of such a function ? This is questionable ! Why not a one year period, ore else ? Are you sure that the problem requires such a sinusoidal model ? If statistical computations have to be carried out, why not directly using the given data instead of an intermediate function with, may be, no real significance!
answered May 17 '14 at 10:16
JJacquelinJJacquelin
45.1k21855
edited May 17 '14 at 23:08
answered May 17 '14 at 10:16
JJacquelinJJacquelin
45.1k21855
answered May 17 '14 at 10:16
JJacquelinJJacquelin
45.1k21855
answered May 17 '14 at 10:16
JJacquelinJJacquelin
45.1k21855
45.1k21855
add a comment |
add a comment |
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$begingroup$
What do you mean by fitting? @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:45
$begingroup$
We haven't really learned one that would work for this. I am currently in Algebra II Trigonometry honors. My method for attacking this was realizing that the relative maximums and minimums change by -52,000 and +8,000 respectively each 10 years. Then I tried to work that into the normal A·(sin or cos)(bx+c)+d. @Amzoti
$endgroup$
– John Smith
May 15 '14 at 3:51