3. Choose a country and research population data in order to fill out the table below INIDA a. Copy the population numbers counted each five years, as shown in the data base, for the years from 1950 to 2000. Add a column, t, measuring years since 1945. Year t population 1950 5 376,325,200 1955 5 409,880,595 1960 5 450,547,679 1965 5 499,123,324 1970 5 555,189,792 1975 5 623,102,897 1980 5 698,952,844 1985 5 784,360,008 1990 5 873,277,798 1995 5 963,922,588 2000 5 1,056,575,549 b. What is the country you selected? In what part of the world is it? What is the magnitude of its population numbers? (100,000’s, millions, hundred millions, billions?) Is it growing or shrinking in population size? c. Enter years since 1945 and your population numbers into your graphing calculator. Create a scatterplot of the data. Is the data growing or shrinking? Does it appear to be a linear pattern or non-linear? Explain your conclusions. d. Use your calculator to fit a linear model to the population size. i. Write the equation of the linear regression and superimpose its graph on your scatterplot. ii. Use TI-Connect to copy the scatterplot onto your write-up, or just draw a sketch of it. iii. How well does the linear model fit your data? iv. What is the vertical intercept of the regression model? What does it mean in the context of the population? v. What is the slope of the regression model? What does it mean in the context of the population? vi. Use the model to predict the population size in the year you were born. Also, use the model to predict the population size in the year 2007. e. Next fit an exponential model to your population data. i. Write the equation of the exponential regression and superimpose its graph on your scatterplot. ii. How well does the exponential model fit your data? By looking at the graphs, does it appear that the exponential model fits better than the linear model? f. Next fit a power function to your population data. i. Write the equation of the power regression and superimpose its graph on your scatterplot. ii. How well does the power model fit your data? By looking at the graphs, which of the three models seems to fit the best? g. Find the linear correlation coefficient for each model and compare them to determine which model fits the data best.
3. Choose a country and research population data in order to fill out the table below INIDA a. Copy the population numbers counted each five years, as shown in the data base, for the years from 1950 to 2000. Add a column, t, measuring years since 1945. Year t population 1950 5 376,325,200 1955 5 409,880,595 1960 5 450,547,679 1965 5 499,123,324 1970 5 555,189,792 1975 5 623,102,897 1980 5 698,952,844 1985 5 784,360,008 1990 5 873,277,798 1995 5 963,922,588 2000 5 1,056,575,549 b. What is the country you selected? In what part of the world is it? What is the magnitude of its population numbers? (100,000’s, millions, hundred millions, billions?) Is it growing or shrinking in population size? c. Enter years since 1945 and your population numbers into your graphing calculator. Create a scatterplot of the data. Is the data growing or shrinking? Does it appear to be a linear pattern or non-linear? Explain your conclusions. d. Use your calculator to fit a linear model to the population size. i. Write the equation of the linear regression and superimpose its graph on your scatterplot. ii. Use TI-Connect to copy the scatterplot onto your write-up, or just draw a sketch of it. iii. How well does the linear model fit your data? iv. What is the vertical intercept of the regression model? What does it mean in the context of the population? v. What is the slope of the regression model? What does it mean in the context of the population? vi. Use the model to predict the population size in the year you were born. Also, use the model to predict the population size in the year 2007. e. Next fit an exponential model to your population data. i. Write the equation of the exponential regression and superimpose its graph on your scatterplot. ii. How well does the exponential model fit your data? By looking at the graphs, does it appear that the exponential model fits better than the linear model? f. Next fit a power function to your population data. i. Write the equation of the power regression and superimpose its graph on your scatterplot. ii. How well does the power model fit your data? By looking at the graphs, which of the three models seems to fit the best? g. Find the linear correlation coefficient for each model and compare them to determine which model fits the data best.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.2: Exponents And Radicals
Problem 82E
Related questions
Question
ONLY f, fi, fii
3. Choose a country and research population data in order to fill out the table below INIDA
a. Copy the population numbers counted each five years, as shown in the data base, for
the years from 1950 to 2000. Add a column, t, measuring years since 1945.
3. Choose a country and research population data in order to fill out the table below INIDA
a. Copy the population numbers counted each five years, as shown in the data base, for
the years from 1950 to 2000. Add a column, t, measuring years since 1945.
Year | t | population |
1950 | 5 | 376,325,200 |
1955 | 5 | 409,880,595 |
1960 | 5 | 450,547,679 |
1965 | 5 | 499,123,324 |
1970 | 5 | 555,189,792 |
1975 | 5 | 623,102,897 |
1980 | 5 | 698,952,844 |
1985 | 5 | 784,360,008 |
1990 | 5 | 873,277,798 |
1995 | 5 | 963,922,588 |
2000 | 5 | 1,056,575,549 |
b. What is the country you selected? In what part of the world is it? What is the magnitude
of its population numbers? (100,000’s, millions, hundred millions, billions?) Is it growing or
shrinking in population size?
c. Enter years since 1945 and your population numbers into your graphing calculator.
Create a scatterplot of the data. Is the data growing or shrinking? Does it appear to be a
linear pattern or non-linear? Explain your conclusions.
d. Use your calculator to fit a linear model to the population size.
i. Write the equation of the linear regression and superimpose its graph on your scatterplot.
ii. Use TI-Connect to copy the scatterplot onto your write-up, or just draw a sketch of it.
iii. How well does the linear model fit your data?
iv. What is the vertical intercept of the regression model? What does it mean in the context
of the population?
v. What is the slope of the regression model? What does it mean in the context of the
population?
vi. Use the model to predict the population size in the year you were born. Also, use the
model to predict the population size in the year 2007.
e. Next fit an exponential model to your population data.
i. Write the equation of the exponential regression and superimpose its graph on your
scatterplot.
ii. How well does the exponential model fit your data? By looking at the graphs, does it
appear that the exponential model fits better than the linear model?
f. Next fit a powerfunction to your population data.
i. Write the equation of the power regression and superimpose its graph on your
scatterplot.
ii. How well does the power model fit your data? By looking at the graphs, which of the
three models seems to fit the best?
g. Find the linearcorrelation coefficient for each model and compare them to determine
which model fits the data best.
of its population numbers? (100,000’s, millions, hundred millions, billions?) Is it growing or
shrinking in population size?
c. Enter years since 1945 and your population numbers into your graphing calculator.
Create a scatterplot of the data. Is the data growing or shrinking? Does it appear to be a
linear pattern or non-linear? Explain your conclusions.
d. Use your calculator to fit a linear model to the population size.
i. Write the equation of the linear regression and superimpose its graph on your scatterplot.
ii. Use TI-Connect to copy the scatterplot onto your write-up, or just draw a sketch of it.
iii. How well does the linear model fit your data?
iv. What is the vertical intercept of the regression model? What does it mean in the context
of the population?
v. What is the slope of the regression model? What does it mean in the context of the
population?
vi. Use the model to predict the population size in the year you were born. Also, use the
model to predict the population size in the year 2007.
e. Next fit an exponential model to your population data.
i. Write the equation of the exponential regression and superimpose its graph on your
scatterplot.
ii. How well does the exponential model fit your data? By looking at the graphs, does it
appear that the exponential model fits better than the linear model?
f. Next fit a power
i. Write the equation of the power regression and superimpose its graph on your
scatterplot.
ii. How well does the power model fit your data? By looking at the graphs, which of the
three models seems to fit the best?
g. Find the linear
which model fits the data best.
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