The following data represent the population of a country. An ecologist is interested in building a model that describes the population. Year, x 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Population, y 76,212,200 92,228,500 106,021,500 123,202,600 132,164,600 151,325,800 179,323,200 203,302,000 226,542,200 248,709,900 281,421,900 1 (a) Treating the year as the independent variable and the population as the dependent variable, use a graphing utility to fit a logistic model from the data. Find the values for a, b and c in a logistic model of C the form y = 1 + ae bx a = (Use scientific notation. Round to five decimal places as needed.) b = (Round to four decimal places as needed.) C= (Round to one decimal place as needed.)
The following data represent the population of a country. An ecologist is interested in building a model that describes the population. Year, x 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000 Population, y 76,212,200 92,228,500 106,021,500 123,202,600 132,164,600 151,325,800 179,323,200 203,302,000 226,542,200 248,709,900 281,421,900 1 (a) Treating the year as the independent variable and the population as the dependent variable, use a graphing utility to fit a logistic model from the data. Find the values for a, b and c in a logistic model of C the form y = 1 + ae bx a = (Use scientific notation. Round to five decimal places as needed.) b = (Round to four decimal places as needed.) C= (Round to one decimal place as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The following data represent the population of a country.
An ecologist is interested in building a model that describes
the population.
Year, x
1900
1910
1920
1930
1940
1950
1960
1970
1980
1990
2000
Population, y
76,212,200
92,228,500
106,021,500
123,202,600
132,164,600
151,325,800
179,323,200
203,302,000
226,542,200
248,709,900
281,421,900
(a) Treating the year as the independent variable
and the population as the dependent variable, use
a graphing utility to fit a logistic model from the
data.
Find the values for a, b and c in a logistic model of
the form y =
C
1 + ae
-bx
a =
(Use scientific notation. Round to five decimal
places as needed.)
b=
(Round to four decimal places as needed.)
C=
(Round to one decimal place as needed.)
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