The United States Census Bureau provided the following estimates and predic- tions for the total world population (* data from 2012, 2020-2050 numbers are predictions). Year Population 1950 2,556,518,868 1960 3,040,617,514 1970 3,707,921,742 1980 4,447,068,714 1990 5,274,320,491 2000 6,073,265,234 2010 6,838,220,183 2020* 7,608,075,253 2030* 8,295,925,812 2040* 8,897,180,403 2050* 9,404,296,384
The United States Census Bureau provided the following estimates and predic- tions for the total world population (* data from 2012, 2020-2050 numbers are predictions).
Year Population
1950 2,556,518,868 1960 3,040,617,514 1970 3,707,921,742 1980 4,447,068,714 1990 5,274,320,491 2000 6,073,265,234 2010 6,838,220,183
2020* 7,608,075,253 2030* 8,295,925,812 2040* 8,897,180,403 2050* 9,404,296,384
Two major models used in predicting population growths are the Exponential Model P(t) = P0ert
and the Logistic Model
P(t) = k
1 + be−ct
Let t = 0 represent the year 1950 and plot the given dataset in a graph with viewing dimensions [−10, 110] for the x-coordinate and [0, 1010] for the y-coordinate.
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In a paragraph discuss the properties of both models, then explain why one of the models fits the dataset better. Things you should touch upon in your explanations include but are not limited to: Assumptions being made by the model on the dataset, The behavior of the model with respect to the shape of the graph. After choosing a model, using a graphing calculator find parameters for the chosen model that best fit the dataset and graph this alongside the original data.
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