The population of the US in the years 1953, 1964, 1982, 1990, 2000 and 2010 is given in the table...
The population of the US in the years 1953, 1964,
1982, 1990, 2000 and 2010 is given
in the table below.
year population of the US
1953 582603417
1964 694581759
1982 1008175288
1990 1133682501
2000 1265830000
Use Lagrange polynomials to:
(a) construct the quartic polynomial that passes through the data
for the years 1953, 1964,
1982, 1990 and 2000.
(b) construct the quintic polynomial that passes through the data
for the years 1953, 1964,
1982, 1990, 2000 and 2010
Homework Answers
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The population of the US in the years 1953, 1964, 1982, 1990, 2000 and 2010 is given in the table...
Year Population in Millions GDP in Trillions of US$ 2014 318.86 16.29 2011 311.72 15.19 2010...
Year Population in Millions GDP in Trillions of US$ 2014 318.86 16.29 2011 311.72 15.19 2010 309.35 14.94 2009 306.77 14.54 2008 304.09 14.58 2006 298.38 14.72 2004 292.81 13.95 2003 290.11 13.53 2002 287.63 12.96 2001 284.97 12.71 2000 1999 279.04 12.32 1998 275.85 11.77 1990 249.62 8.91 1989 246.82 8.85 1987 242.29 8.29 1986 240.13 7.94 1985 237.92 7.71 1984 235.82 7.4 1982 231.66 6.49 1981 229.47 6.59 1980 6.5 1979 225.06 6.5 1977 220.24 6.02 1976 218.04...
how? 9. In 2015, 88% of US residents used the internet. The table shows the percent who use the internet for selected years from 2000 and projected to 2025. Year Percent 2000 67 2015 2010 82 79 9...
how?
9. In 2015, 88% of US residents used the internet. The table shows the percent who use the internet for selected years from 2000 and projected to 2025. Year Percent 2000 67 2015 2010 82 79 95 98 (a) Use your calculator to find the natural logarithmic function that models the percent p as a func- tion of x, the number of years after 1990. Report the model with 4 significant digit coefficients. (b) Use the model to predict...
A country's census lists the population of the country as 242 million in 1990, 286 million...
A country's census lists the population of the country as 242 million in 1990, 286 million in 2000, and 322 million in 2010. Fit a second- degree polynomial passing through these three points. (Let the year 2000 be x 0 and let p(x) represent the population in millions.) p(x) million Use this polynomial to predict the populations in 2020 and in 2030. 2020 2030 million million
12. In 2015, 88% of US residents used the internet, up from 14% in 1995 The table shows the percent who use the internet for selected years from 2000 and projected to 2025. Year 2000 2005 2010 20...
12. In 2015, 88% of US residents used the internet, up from 14% in 1995 The table shows the percent who use the internet for selected years from 2000 and projected to 2025. Year 2000 2005 2010 2015 2020 2025 Percent 67 79 82 88 95 98 Find the logarithmic function that models the percent p as a function of x, the number of years after 1990. State the correlation coefficient. a) b) Use the model to predict the percentage...
please dont use any program while solving it, but if you want to use maple, thats...
please dont use any program while solving it, but if you want
to use maple, thats fine.
The following table lists the population of the United States from 1960 to 2010. Year 1960 1970 1980 1990 2000 2010 Population (thousands) OD 179,323 to 203,302 226,542 249,633 281,442 307,746 a. Find the Lagrange polynomial of degree 5 fitting this data and use this polynomial to estimate the population in the years 1950, 1975, and 2020. b. The population in 1950 was...
The population of a certain state (in thousands) from 1990 (t = 0) to 2000 (t=...
The population of a certain state (in thousands) from 1990 (t = 0) to 2000 (t= 10) is modeled by the polynomial p(t) = -0.376+ 108t + 7066. a. Determine the average growth rate from 1990 to 2000. b. What was the growth rate for this state in 1994 (t = 4) and 2000 (t = 10)? c. Use a graphing utility to graph p' for Osts 10. What does this graph tell you about population growth in this state...
Price in 1990 Price in 2000 | 12 Price in 2010 10. 14 Pen Shirt Shoe...
Price in 1990 Price in 2000 | 12 Price in 2010 10. 14 Pen Shirt Shoe Pair 15 17 16 18 2018 Use the table above. Suppose your market basket is 10 pens, 5 shirts, and 3 pairs of shoes. 1. What is the approximate percentage change in prices between 2010 and 2000, when 1990 is the base year? (a) 235 (b) 24.33 (c) 16.59 (d) 5.97
The table below gives the estimated world population (in billions) for various years. Year 1980 1990...
The table below gives the estimated world population (in billions) for various years. Year 1980 1990 1997 2000 2005 2011 Population 4400 5100 5852 6080 6450 7000 Linear Regression Equation: ____________________ Correlation Coefficient (r): _________ Type of Correlation: ______________________ Is the correlation strong? Explain Using the linear regression equation predict the world population in the year 2015.
Year Population 1900 200507 1910 430980 1920 732016 1930 1265258 1940 1394711 1950 1451277 1960 1424815 1970 1471701 1980 1168972 1990 1203789 2000 1332650 2010...
Year Population
1900 200507
1910 430980
1920 732016
1930 1265258
1940 1394711
1950 1451277
1960 1424815
1970 1471701
1980 1168972
1990 1203789
2000 1332650
2010 1385108
the census populations of the Bronx from 1900 to 2010 is given
above. Estimate the Bronx's 2005 population using the following
methods:
(a) Linear interpolation interp1 (year, population, 2005)) (b) Polynomial interpolation of just the last three censuses (polyval and polyfit) (c) Polynomial interpolation of all the censuses (d) Second-degree polynomial regression (not interpolation;...
.. In 2000, the population of a country was approximately 5.73 million and by 2028 it...
.. In 2000, the population of a country was approximately 5.73 million and by 2028 it is projected to grow to 8 million. Use the exponential growth model A=Age, in which t is the number of years after 2000 and A, is in millions, to find an exponential growth function that models the data, By which year will the population be 15 million? Population (millions) b. 12 Projected 9 2000 6 5,730,000 3- 0- 1950 1970 1990 2010 2030 2050...
how?
9. In 2015, 88% of US residents used the internet. The table shows the percent who use the internet for selected years from 2000 and projected to 2025. Year Percent 2000 67 2015 2010 82 79 95 98 (a) Use your calculator to find the natural logarithmic function that models the percent p as a func- tion of x, the number of years after 1990. Report the model with 4 significant digit coefficients. (b) Use the model to predict...
A country's census lists the population of the country as 242 million in 1990, 286 million in 2000, and 322 million in 2010. Fit a second- degree polynomial passing through these three points. (Let the year 2000 be x 0 and let p(x) represent the population in millions.) p(x) million Use this polynomial to predict the populations in 2020 and in 2030. 2020 2030 million million
12. In 2015, 88% of US residents used the internet, up from 14% in 1995 The table shows the percent who use the internet for selected years from 2000 and projected to 2025. Year 2000 2005 2010 2015 2020 2025 Percent 67 79 82 88 95 98 Find the logarithmic function that models the percent p as a function of x, the number of years after 1990. State the correlation coefficient. a) b) Use the model to predict the percentage...
please dont use any program while solving it, but if you want
to use maple, thats fine.
The following table lists the population of the United States from 1960 to 2010. Year 1960 1970 1980 1990 2000 2010 Population (thousands) OD 179,323 to 203,302 226,542 249,633 281,442 307,746 a. Find the Lagrange polynomial of degree 5 fitting this data and use this polynomial to estimate the population in the years 1950, 1975, and 2020. b. The population in 1950 was...
The population of a certain state (in thousands) from 1990 (t = 0) to 2000 (t= 10) is modeled by the polynomial p(t) = -0.376+ 108t + 7066. a. Determine the average growth rate from 1990 to 2000. b. What was the growth rate for this state in 1994 (t = 4) and 2000 (t = 10)? c. Use a graphing utility to graph p' for Osts 10. What does this graph tell you about population growth in this state...
Price in 1990 Price in 2000 | 12 Price in 2010 10. 14 Pen Shirt Shoe Pair 15 17 16 18 2018 Use the table above. Suppose your market basket is 10 pens, 5 shirts, and 3 pairs of shoes. 1. What is the approximate percentage change in prices between 2010 and 2000, when 1990 is the base year? (a) 235 (b) 24.33 (c) 16.59 (d) 5.97
Year Population
1900 200507
1910 430980
1920 732016
1930 1265258
1940 1394711
1950 1451277
1960 1424815
1970 1471701
1980 1168972
1990 1203789
2000 1332650
2010 1385108
the census populations of the Bronx from 1900 to 2010 is given
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methods:
(a) Linear interpolation interp1 (year, population, 2005)) (b) Polynomial interpolation of just the last three censuses (polyval and polyfit) (c) Polynomial interpolation of all the censuses (d) Second-degree polynomial regression (not interpolation;...
.. In 2000, the population of a country was approximately 5.73 million and by 2028 it is projected to grow to 8 million. Use the exponential growth model A=Age, in which t is the number of years after 2000 and A, is in millions, to find an exponential growth function that models the data, By which year will the population be 15 million? Population (millions) b. 12 Projected 9 2000 6 5,730,000 3- 0- 1950 1970 1990 2010 2030 2050...
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