This exercise deals with data from the U.S. Bureau of the Census
on populations of major cities.† These data allow us to find how
fast the population is growing and when it will reach certain
levels. Such calculations are very important, because they indicate
the future needs of the population for goods and services and how
well the area can support the population.
The third largest city in the United States is Chicago. Its
population in 2011 was 2,705 (in thousands); in 2012, it was
2,715.
(a) Develop the model that represents the population of Chicago.
(Write your model in terms of t, where t is the
number of years after 2011. Let p represent the population
in thousands. Round the coefficient of t to seven decimal
places.)
p(t) =
(b) Predict the population in 2019. (Round your answer up to the
nearest whole number.)
(c) Predict the population in 2023. (Round your answer up to the
nearest whole number.)
thousand people
(d) Predict when the population will be double its 2011 population.
(Round your answer to one decimal place.)
years after 2011
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