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10 5 population in 2010 2015 and 2020 2 World Population The following table shows...

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Calculus

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10 5 population in 2010 2015 and 2020 2 World Population The following table shows U S Census Bureau estimates for key world population benchmarks A geometric sequence is the discrete analog to an exponent function Both a geometric sequence and exponent function assume a constant multiplicative rate of change Let w be a geometric sequence that represents the world population in billions of persons n years after 1959 Use w 3 00 as the initial condition for the sequence Population in billions Year 1959 1974 1987 1999 2012 345 6 a Assuming an annual percentage increase of 1 62 in world population write a recursive formula for the sequence w b Write an explicit formula for the geometric sequence w in part a Use exponential regression to confirm the accuracy of this model c Use the formulas from parts a and b to estimate the world population in 2010 2015 and 2020 d The actual annual growth rate in world population has slowed from 2 22 in 1963 to 1 09 in 2013 so a logistic growth model may be more appropriate than an exponential model Use the data in the table and logistic regrosci to optimate the world

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